메뉴 건너뛰기




Volumn 356, Issue 6, 2002, Pages 367-474

Predictability: A way to characterize complexity

Author keywords

Algorithmic complexity; High dimensional chaos; Predictability; Turbulence

Indexed keywords


EID: 0000712133     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0370-1573(01)00025-4     Document Type: Review
Times cited : (337)

References (234)
  • 5
    • 49049151403 scopus 로고
    • Symbolic dynamics and hyperbolic dynamic-systems
    • V.M. Alekseev, M.V. Yakobson, Symbolic dynamics and hyperbolic dynamic-systems, Phys. Rep. 75 (1981) 287.
    • (1981) Phys. Rep. , vol.75 , pp. 287
    • Alekseev, V.M.1    Yakobson, M.V.2
  • 6
  • 9
    • 0024088719 scopus 로고
    • The onset and spatial development of turbulence in flow systems
    • I.S. Arason, A.V. Gaponov-Grekhov, M. Rabinovich, The onset and spatial development of turbulence in flow systems, Physica D 33 (1988) 1.
    • (1988) Physica D , vol.33 , pp. 1
    • Arason, I.S.1    Gaponov-Grekhov, A.V.2    Rabinovich, M.3
  • 10
    • 0031280861 scopus 로고    scopus 로고
    • Dispersion of passive tracers in closed basins: Beyond the diffusion coefficient
    • V. Artale, G. Boffetta, A. Celani, M. Cencini, A. Vulpiani, Dispersion of passive tracers in closed basins: Beyond the diffusion coefficient, Phys. Fluids A 9 (1997) 3162.
    • (1997) Phys. Fluids A , vol.9 , pp. 3162
    • Artale, V.1    Boffetta, G.2    Celani, A.3    Cencini, M.4    Vulpiani, A.5
  • 12
    • 0031556902 scopus 로고    scopus 로고
    • Predictability in the large: An extension of the concept of Lyapunov exponent
    • E. Aurell, G. Boffetta, A. Crisanti, G. Paladin, A. Vulpiani, Predictability in the large: an extension of the concept of Lyapunov exponent, J. Phys. A 30 (1997) 1.
    • (1997) J. Phys. A , vol.30 , pp. 1
    • Aurell, E.1    Boffetta, G.2    Crisanti, A.3    Paladin, G.4    Vulpiani, A.5
  • 14
    • 5844290410 scopus 로고
    • Self-organized criticality an explanation of 1/f noise
    • P. Bak, C. Tang, K. Wiesenfeld, Self-organized criticality an explanation of 1/f noise, Phys. Rev. Lett. 59 (1987) 381.
    • (1987) Phys. Rev. Lett. , vol.59 , pp. 381
    • Bak, P.1    Tang, C.2    Wiesenfeld, K.3
  • 16
    • 0001954206 scopus 로고
    • Damage spreading and Lyapunov exponent in cellular automata
    • F. Bagnoli, R. Rechtman, S. Ruffo, Damage spreading and Lyapunov exponent in cellular automata, Phys. Lett. A 172 (1992) 34.
    • (1992) Phys. Lett. A , vol.172 , pp. 34
    • Bagnoli, F.1    Rechtman, R.2    Ruffo, S.3
  • 17
    • 0001505329 scopus 로고    scopus 로고
    • Synchronization and maximum Lyapunov exponent in cellular automata
    • F. Bagnoli, R. Rechtman, Synchronization and maximum Lyapunov exponent in cellular automata, Phys. Rev. E 59 (1999) R1307.
    • (1999) Phys. Rev. E , vol.59
    • Bagnoli, F.1    Rechtman, R.2
  • 18
    • 0019637009 scopus 로고
    • A study of barotropic model flows: Intermittency, waves and predictability
    • C. Basdevant, B. Legras, R. Sadourny, M. Beland, A study of barotropic model flows: intermittency, waves and predictability, J. Atmos. Sci. 38 (1981) 2305.
    • (1981) J. Atmos. Sci. , vol.38 , pp. 2305
    • Basdevant, C.1    Legras, B.2    Sadourny, R.3    Beland, M.4
  • 20
    • 0018989294 scopus 로고
    • Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems: A method for computing all of them
    • G. Benettin, L. Galgani, A. Giorgilli, J.M. Strelcyn, Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems: a method for computing all of them, Meccanica 15 (1980) 9.
    • (1980) Meccanica , vol.15 , pp. 9
    • Benettin, G.1    Galgani, L.2    Giorgilli, A.3    Strelcyn, J.M.4
  • 21
    • 85054432388 scopus 로고
    • How to define complexity in physics and why
    • W.H. Zurek (Ed.), Addison-Wesley, Redwood City
    • C.H. Bennet, How to define complexity in physics and why, in: W.H. Zurek (Ed.), Complexity, Entropy and the Physics of Information, Addison-Wesley, Redwood City, 1990, p. 137.
    • (1990) Complexity, Entropy and the Physics of Information , pp. 137
    • Bennet, C.H.1
  • 22
    • 18844405278 scopus 로고
    • On the multifractal nature of fully developed turbulence and chaotic systems
    • R. Benzi, G. Paladin, G. Parisi, A. Vulpiani, On the multifractal nature of fully developed turbulence and chaotic systems, J. Phys. A 17 (1984) 3521.
    • (1984) J. Phys. A , vol.17 , pp. 3521
    • Benzi, R.1    Paladin, G.2    Parisi, G.3    Vulpiani, A.4
  • 23
    • 36149037990 scopus 로고
    • Characterization of intermittency in chaotic systems
    • R. Benzi, G. Paladin, G. Parisi, A. Vulpiani, Characterization of intermittency in chaotic systems, J. Phys. A 18 (1985) 2157.
    • (1985) J. Phys. A , vol.18 , pp. 2157
    • Benzi, R.1    Paladin, G.2    Parisi, G.3    Vulpiani, A.4
  • 24
    • 0004671466 scopus 로고    scopus 로고
    • Intermittency and eddy-viscosities in dynamical models of turbulence
    • R. Benzi, L. Biferale, S. Succi, F. Toschi, Intermittency and eddy-viscosities in dynamical models of turbulence, Phys. Fluids 11 (1998) 1221.
    • (1998) Phys. Fluids , vol.11 , pp. 1221
    • Benzi, R.1    Biferale, L.2    Succi, S.3    Toschi, F.4
  • 25
    • 20644470598 scopus 로고
    • The mechanism of the stochastic resonance
    • R. Benzi, A. Sutera, A. Vulpiani, The mechanism of the stochastic resonance, J. Phys. A 14 (1981) L453.
    • (1981) J. Phys. A , vol.14
    • Benzi, R.1    Sutera, A.2    Vulpiani, A.3
  • 26
  • 28
    • 0000775539 scopus 로고
    • An observation probability density equations, or, when simulations reproduce statistics?
    • G. Berkooz, An observation probability density equations, or, when simulations reproduce statistics?, Nonlinearity 7 (1994) 313.
    • (1994) Nonlinearity , vol.7 , pp. 313
    • Berkooz, G.1
  • 30
    • 0003434405 scopus 로고    scopus 로고
    • Exit time of turbulent signals: A way to detect the Intermediate Dissipative Range
    • L. Biferale, M. Cencini, D. Vergni, A. Vulpiani, Exit time of turbulent signals: a way to detect the Intermediate Dissipative Range, Phys. Rev. E 60 (1999) R6295.
    • (1999) Phys. Rev. E , vol.60
    • Biferale, L.1    Cencini, M.2    Vergni, D.3    Vulpiani, A.4
  • 32
    • 0038710050 scopus 로고    scopus 로고
    • Strong chaos without butterfly effect in dynamical systems with feedback
    • G. Boffetta, G. Paladin, A. Vulpiani, Strong chaos without butterfly effect in dynamical systems with feedback, J. Phys. A 29 (1996) 2291.
    • (1996) J. Phys. A , vol.29 , pp. 2291
    • Boffetta, G.1    Paladin, G.2    Vulpiani, A.3
  • 34
    • 0001891382 scopus 로고    scopus 로고
    • Inverse energy cascade in two-dimensional turbulence: Deviations from Gaussian behavior
    • G. Boffetta, A. Celani, M. Vergassola, Inverse energy cascade in two-dimensional turbulence: deviations from Gaussian behavior, Phys. Rev. E 61 (2000) R29.
    • (2000) Phys. Rev. E , vol.61
    • Boffetta, G.1    Celani, A.2    Vergassola, M.3
  • 36
    • 0034711899 scopus 로고    scopus 로고
    • The predictability problem in systems with an uncertainty in the evolution law
    • G. Boffetta, A. Celani, M. Cencini, G. Lacorata, A. Vulpiani, The predictability problem in systems with an uncertainty in the evolution law, J. Phys. A 33 (2000) 1313.
    • (2000) J. Phys. A , vol.33 , pp. 1313
    • Boffetta, G.1    Celani, A.2    Cencini, M.3    Lacorata, G.4    Vulpiani, A.5
  • 37
    • 0035322317 scopus 로고    scopus 로고
    • Predictability of the energy cascade in 2D turbulence
    • G. Boffetta, S. Musacchio, Predictability of the energy cascade in 2D turbulence, Phys. Fluids 13 (2000) 1060.
    • (2000) Phys. Fluids , vol.13 , pp. 1060
    • Boffetta, G.1    Musacchio, S.2
  • 39
    • 44949285418 scopus 로고
    • A mechanism for localized turbulence
    • T. Bohr, D. Rand, A mechanism for localized turbulence, Physica D 52 (1991) 532.
    • (1991) Physica D , vol.52 , pp. 532
    • Bohr, T.1    Rand, D.2
  • 41
    • 0001300739 scopus 로고
    • Markov partitions for Axiom-A diffeomorphisms
    • R. Bowen, Markov partitions for Axiom-A diffeomorphisms, Amer. J. Math. 92 (1970) 725.
    • (1970) Amer. J. Math. , vol.92 , pp. 725
    • Bowen, R.1
  • 42
    • 0000340279 scopus 로고
    • Entropy and the complexity of the trajectories of a dynamical system
    • A.A. Brudno, Entropy and the complexity of the trajectories of a dynamical system, Trans. Moscow Math. Soc. 44 (1983) 127.
    • (1983) Trans. Moscow Math. Soc. , vol.44 , pp. 127
    • Brudno, A.A.1
  • 43
    • 5244293562 scopus 로고
    • Noise effects in a non-linear dynamic system - The RF - Superconducting quantum interference device
    • A.R. Bulsara, E.W. Jacobs, W.C. Schieve, Noise effects in a non-linear dynamic system - the RF - superconducting quantum interference device, Phys. Rev. A 42 (1990) 4614.
    • (1990) Phys. Rev. A , vol.42 , pp. 4614
    • Bulsara, A.R.1    Jacobs, E.W.2    Schieve, W.C.3
  • 46
    • 2542514820 scopus 로고    scopus 로고
    • Dynamical properties and predictability of a class of self-organized critical models
    • E. Caglioti, V. Loreto, Dynamical properties and predictability of a class of self-organized critical models, Phys. Rev. E 53 (1996) 2953.
    • (1996) Phys. Rev. E , vol.53 , pp. 2953
    • Caglioti, E.1    Loreto, V.2
  • 47
    • 0040713763 scopus 로고
    • Partitions, rational partitions, and characterization of complexity
    • M. Casartelli, Partitions, rational partitions, and characterization of complexity, Complex Systems 4 (1990) 491.
    • (1990) Complex Systems , vol.4 , pp. 491
    • Casartelli, M.1
  • 48
    • 0034635284 scopus 로고    scopus 로고
    • Metric features of self-organized criticality states in sandpile models
    • M. Casartelli, M. Zerbini, Metric features of self-organized criticality states in sandpile models, J. Phys. A 33 (2000) 863.
    • (2000) J. Phys. A , vol.33 , pp. 863
    • Casartelli, M.1    Zerbini, M.2
  • 52
    • 10844230120 scopus 로고    scopus 로고
    • A non-linear marginal stability criterion for information propagation
    • in press
    • M. Cencini, A. Torcini, A non-linear marginal stability criterion for information propagation, Phys. Rev. E 63 (2001), in press.
    • (2001) Phys. Rev. E , vol.63
    • Cencini, M.1    Torcini, A.2
  • 53
    • 84918358658 scopus 로고
    • On the length of programs for computing finite binary sequences
    • G.J. Chaitin, On the length of programs for computing finite binary sequences, J. Assoc. Comp. Mach. 13 (1966) 547.
    • (1966) J. Assoc. Comp. Mach. , vol.13 , pp. 547
    • Chaitin, G.J.1
  • 54
    • 0016082450 scopus 로고
    • Information-theoretic limitations of formal systems
    • G.J. Chaitin, Information-theoretic limitations of formal systems, J. Assoc. Comp. Mach. 21 (1974) 403.
    • (1974) J. Assoc. Comp. Mach. , vol.21 , pp. 403
    • Chaitin, G.J.1
  • 55
    • 0012269676 scopus 로고
    • Gödel theorem and information
    • G.J. Chaitin, Gödel theorem and information, Int. J. Theor. Phys. 22 (1982) 941.
    • (1982) Int. J. Theor. Phys. , vol.22 , pp. 941
    • Chaitin, G.J.1
  • 57
    • 0002121327 scopus 로고
    • Stochastic problems in physics and astronomy
    • S. Chandrasekhar, Stochastic problems in physics and astronomy, Rev. Mod. Phys. 15 (1943) 1.
    • (1943) Rev. Mod. Phys. , vol.15 , pp. 1
    • Chandrasekhar, S.1
  • 58
    • 0002204536 scopus 로고
    • Collective behaviors in spatially extended systems with local interactions and synchronous updating
    • H. Chatè, P. Manneville, Collective behaviors in spatially extended systems with local interactions and synchronous updating, Prog. Theor. Phys. 87 (1992) 1.
    • (1992) Prog. Theor. Phys. , vol.87 , pp. 1
    • Chatè, H.1    Manneville, P.2
  • 59
    • 5244229824 scopus 로고
    • Noise-induced instability
    • Z.Y. Chen, Noise-induced instability, Phys. Rev. A 42 (1990) 5837.
    • (1990) Phys. Rev. A , vol.42 , pp. 5837
    • Chen, Z.Y.1
  • 60
    • 10844247904 scopus 로고    scopus 로고
    • Natural laws and human prediction
    • P. Weingartner, G. Schurz (Eds.), Springer, Berlin
    • B.V. Chirikov, Natural Laws and Human Prediction, in: P. Weingartner, G. Schurz (Eds.), Laws and Prediction in the Light of Chaos Research, Springer, Berlin, 1996, p. 10.
    • (1996) Laws and Prediction in the Light of Chaos Research , pp. 10
    • Chirikov, B.V.1
  • 61
    • 0000842022 scopus 로고
    • Computing the Kolmogorov entropy from time signals of dissipative and conservative dynamical systems
    • A. Cohen, I. Procaccia, Computing the Kolmogorov entropy from time signals of dissipative and conservative dynamical systems, Phys. Rev. A 31 (1985) 1872.
    • (1985) Phys. Rev. A , vol.31 , pp. 1872
    • Cohen, A.1    Procaccia, I.2
  • 62
    • 0033130277 scopus 로고    scopus 로고
    • The definition and measurement of the topological entropy per unit volume in parabolic PDEs
    • P. Collet, J.P. Eckmann, The definition and measurement of the topological entropy per unit volume in parabolic PDEs, Nonlinearity 12 (1999) 451.
    • (1999) Nonlinearity , vol.12 , pp. 451
    • Collet, P.1    Eckmann, J.P.2
  • 63
    • 0042452724 scopus 로고
    • Invariant cycles in the random mapping of N integers onto themselves. Comparison with Kauffman binary network
    • E. Bienenstock et al. (Eds.), Springer, Berlin
    • J. Coste, M. Hénon, Invariant cycles in the random mapping of N integers onto themselves. Comparison with Kauffman binary network, in: E. Bienenstock et al. (Eds.), Disordered Systems and Biological Organization, Springer, Berlin, 1986, p. 360.
    • (1986) Disordered Systems and Biological Organization , pp. 360
    • Coste, J.1    Hénon, M.2
  • 64
    • 4244210758 scopus 로고
    • On the effects of an uncertainty on the evolution law in dynamical systems
    • A. Crisanti, M. Falcioni, A. Vulpiani, On the effects of an uncertainty on the evolution law in dynamical systems, Physica A 160 (1989) 482.
    • (1989) Physica A , vol.160 , pp. 482
    • Crisanti, A.1    Falcioni, M.2    Vulpiani, A.3
  • 65
    • 0040282818 scopus 로고
    • Applying algorithmic complexity to define chaos in the motion of complex systems
    • A. Crisanti, M. Falcioni, G. Mantica, A. Vulpiani, Applying algorithmic complexity to define chaos in the motion of complex systems, Phys. Rev. E 50 (1994) 1959.
    • (1994) Phys. Rev. E , vol.50 , pp. 1959
    • Crisanti, A.1    Falcioni, M.2    Mantica, G.3    Vulpiani, A.4
  • 67
    • 0001570882 scopus 로고    scopus 로고
    • Broken ergodicity and glassy behavior in a deterministic chaotic map
    • A. Crisanti, M. Falcioni, A. Vulpiani, Broken ergodicity and glassy behavior in a deterministic chaotic map, Phys. Rev. Lett. 76 (1996) 612.
    • (1996) Phys. Rev. Lett. , vol.76 , pp. 612
    • Crisanti, A.1    Falcioni, M.2    Vulpiani, A.3
  • 68
    • 12044252828 scopus 로고
    • Pattern formation outside of equilibrium
    • M.C. Cross, P.H. Hohenberg, Pattern formation outside of equilibrium, Rev. Mod. Phys. 65 (1993) 851.
    • (1993) Rev. Mod. Phys. , vol.65 , pp. 851
    • Cross, M.C.1    Hohenberg, P.H.2
  • 69
    • 0001218880 scopus 로고
    • Are attractors relevant for turbulence?
    • J.P. Crutchfield, K. Kaneko, Are attractors relevant for turbulence?, Phys. Rev. Lett. 60 (1988) 2715.
    • (1988) Phys. Rev. Lett. , vol.60 , pp. 2715
    • Crutchfield, J.P.1    Kaneko, K.2
  • 71
    • 0001890111 scopus 로고
    • Velocity-dependent Lyapunov exponents as a measure of chaos for open-flow systems
    • R.J. Deissler, K. Kaneko, Velocity-dependent Lyapunov exponents as a measure of chaos for open-flow systems, Phys. Lett. A 119 (1987) 397.
    • (1987) Phys. Lett. A , vol.119 , pp. 397
    • Deissler, R.J.1    Kaneko, K.2
  • 72
    • 0033613431 scopus 로고    scopus 로고
    • Microscopic chaos from Brownian motion?
    • C. Dettman, E. Cohen, H. van Beijeren, Microscopic chaos from Brownian motion? Nature 401 (1999) 875.
    • (1999) Nature , vol.401 , pp. 875
    • Dettman, C.1    Cohen, E.2    Van Beijeren, H.3
  • 73
    • 0000182409 scopus 로고
    • Generalized Lyapunov exponents corresponding to higher derivatives
    • U. Dressler, J.D. Farmer, Generalized Lyapunov exponents corresponding to higher derivatives, Physica D 59 (1992) 365.
    • (1992) Physica D , vol.59 , pp. 365
    • Dressler, U.1    Farmer, J.D.2
  • 74
    • 35949018382 scopus 로고
    • Ergodic theory of chaos and strange attractors
    • J.P. Eckmann, D. Ruelle, Ergodic theory of chaos and strange attractors, Rev. Mod. Phys. 57 (1985) 617.
    • (1985) Rev. Mod. Phys. , vol.57 , pp. 617
    • Eckmann, J.P.1    Ruelle, D.2
  • 76
    • 4244050656 scopus 로고    scopus 로고
    • Characterization of the spatial complex behavior and transition to chaos in flow systems
    • M. Falcioni, D. Vergni, A. Vulpiani, Characterization of the spatial complex behavior and transition to chaos in flow systems, Physica D 125 (1999) 65.
    • (1999) Physica D , vol.125 , pp. 65
    • Falcioni, M.1    Vergni, D.2    Vulpiani, A.3
  • 77
    • 0026809031 scopus 로고
    • Wavelet transforms and their applications to turbulence
    • M. Farge, Wavelet transforms and their applications to turbulence, Ann. Rev. Fluid Mech. 24 (1992) 395.
    • (1992) Ann. Rev. Fluid Mech. , vol.24 , pp. 395
    • Farge, M.1
  • 79
    • 84957234450 scopus 로고
    • How random is a coin tossing?
    • J. Ford, How random is a coin tossing?, Phys. Today 36 (1983) 40.
    • (1983) Phys. Today , vol.36 , pp. 40
    • Ford, J.1
  • 80
    • 0010681130 scopus 로고
    • Chaos: Solving the Unsolvable, Predicting the Unpredictable
    • M.F. Barnaley, S. Demko (Eds.), Academic Press, New York
    • J. Ford, Chaos: Solving the Unsolvable, Predicting the Unpredictable, in: M.F. Barnaley, S. Demko (Eds.), Chaotic Dynamics and Fractals, Academic Press, New York, 1986.
    • (1986) Chaotic Dynamics and Fractals
    • Ford, J.1
  • 81
    • 44949272611 scopus 로고
    • The Arnold's Cat: Failure of the Correspondence Principle
    • J. Ford, G. Mantica, G.H. Ristow, The Arnold's Cat: Failure of the Correspondence Principle, Physica D 50 (1991) 1493.
    • (1991) Physica D , vol.50 , pp. 1493
    • Ford, J.1    Mantica, G.2    Ristow, G.H.3
  • 82
    • 35949016104 scopus 로고
    • Lattice-gas automata for the Navier-Stokes equation
    • U. Frisch, B. Hasslacher, Y. Pomeau, Lattice-gas automata for the Navier-Stokes equation, Phys. Rev. Lett. 56 (1986) 1505.
    • (1986) Phys. Rev. Lett. , vol.56 , pp. 1505
    • Frisch, U.1    Hasslacher, B.2    Pomeau, Y.3
  • 83
    • 84956236550 scopus 로고
    • A prediction of the multifractal model - The Intermediate Dissipation Range
    • U. Frisch, M. Vergassola, A prediction of the multifractal model - The Intermediate Dissipation Range, Europhys. Lett. 14 (1991) 439.
    • (1991) Europhys. Lett. , vol.14 , pp. 439
    • Frisch, U.1    Vergassola, M.2
  • 85
    • 0000177111 scopus 로고
    • Statistical dynamics generated by fluctuations of local Lyapunov exponents
    • H. Fujisaka, Statistical dynamics generated by fluctuations of local Lyapunov exponents, Prog. Theor. Phys. 70 (1983) 1264.
    • (1983) Prog. Theor. Phys. , vol.70 , pp. 1264
    • Fujisaka, H.1
  • 86
    • 0001536568 scopus 로고
    • Stretching of material lines and surfaces in systems with Lagrangian Chaos
    • S. Galluccio, A. Vulpiani, Stretching of material lines and surfaces in systems with Lagrangian Chaos, Physica A 212 (1994) 75.
    • (1994) Physica A , vol.212 , pp. 75
    • Galluccio, S.1    Vulpiani, A.2
  • 88
    • 0000714969 scopus 로고
    • Une représentation universelle sans invariance globale d'échelle des spectres d'énergie en turbulence développée
    • Y. Gagne, B. Castaing, Une représentation universelle sans invariance globale d'échelle des spectres d'énergie en turbulence développée, C. R. Acad. Sci. Paris 312 (1991) 441.
    • (1991) C. R. Acad. Sci. Paris , vol.312 , pp. 441
    • Gagne, Y.1    Castaing, B.2
  • 89
    • 13844322865 scopus 로고
    • Noise, chaos, and (ε, τ)-entropy per unit time
    • P. Gaspard, X.J. Wang, Noise, chaos, and (ε, τ)-entropy per unit time, Phys. Rep. 235 (1993) 291.
    • (1993) Phys. Rep. , vol.235 , pp. 291
    • Gaspard, P.1    Wang, X.J.2
  • 91
    • 77953468925 scopus 로고
    • Spatio-temporal chaos and localization
    • G. Giacomelli, A. Politi, Spatio-temporal chaos and localization, Europhys. Lett. 15 (1991) 387.
    • (1991) Europhys. Lett. , vol.15 , pp. 387
    • Giacomelli, G.1    Politi, A.2
  • 92
    • 0007091042 scopus 로고
    • Stability and Lyapunov stability of dynamical systems: A differential approach and numerical method
    • I. Goldhirsh, P.L. Sulem, S.A. Orszag, Stability and Lyapunov stability of dynamical systems: a differential approach and numerical method, Physica D 27 (1987) 311.
    • (1987) Physica D , vol.27 , pp. 311
    • Goldhirsh, I.1    Sulem, P.L.2    Orszag, S.A.3
  • 93
  • 94
    • 40749093037 scopus 로고
    • Measuring the strangeness of strange attractors
    • P. Grassberger, I. Procaccia, Measuring the strangeness of strange attractors, Physica D 9 (1983) 189.
    • (1983) Physica D , vol.9 , pp. 189
    • Grassberger, P.1    Procaccia, I.2
  • 95
    • 4243243202 scopus 로고
    • Estimation of the Kolmogorov-entropy from a chaotic signal
    • P. Grassberger, I. Procaccia, Estimation of the Kolmogorov-entropy from a chaotic signal, Phys. Rev. A 28 (1983) 2591.
    • (1983) Phys. Rev. A , vol.28 , pp. 2591
    • Grassberger, P.1    Procaccia, I.2
  • 96
    • 0042317681 scopus 로고
    • Toward a quantitative theory of self-generated complexity
    • P. Grassberger, Toward a quantitative theory of self-generated complexity, Int. J. Theor. Phys. 25 (1986) 907.
    • (1986) Int. J. Theor. Phys. , vol.25 , pp. 907
    • Grassberger, P.1
  • 97
    • 0000187651 scopus 로고
    • Information content and predictability of lumped and distributed dynamical systems
    • P. Grassberger, Information content and predictability of lumped and distributed dynamical systems, Physica Scripta 40 (1989) 346.
    • (1989) Physica Scripta , vol.40 , pp. 346
    • Grassberger, P.1
  • 98
    • 0033613431 scopus 로고    scopus 로고
    • Statistical mechanics - Microscopic chaos from Brownian motion?
    • P. Grassbeger, T. Schreiber, Statistical mechanics - Microscopic chaos from Brownian motion?, Nature 401 (1999) 875.
    • (1999) Nature , vol.401 , pp. 875
    • Grassbeger, P.1    Schreiber, T.2
  • 100
    • 0039117984 scopus 로고
    • Transient, cycles and complexity in cellular automata
    • H.A. Gutowitz, Transient, cycles and complexity in cellular automata, Phys. Rev. A 44 (1991) 7881.
    • (1991) Phys. Rev. A , vol.44 , pp. 7881
    • Gutowitz, H.A.1
  • 101
    • 0001296111 scopus 로고
    • Characterization of on-off intermittency
    • J.F. Heagy, N. Platt, S.M. Hammel, Characterization of on-off intermittency, Phys. Rev. E 49 (1994) 1140.
    • (1994) Phys. Rev. E , vol.49 , pp. 1140
    • Heagy, J.F.1    Platt, N.2    Hammel, S.M.3
  • 102
    • 84943476963 scopus 로고
    • Nonuniform Chaotic dynamics and effects of noise in biochemical systems
    • H. Herzel, W. Ebeling, Th. Schulmeister, Nonuniform Chaotic dynamics and effects of noise in biochemical systems, Z. Naturforsch. A 42 (1987) 136.
    • (1987) Z. Naturforsch. A , vol.42 , pp. 136
    • Herzel, H.1    Ebeling, W.2    Schulmeister, Th.3
  • 103
    • 0000694733 scopus 로고
    • Effects of noise on a non-uniform chaotic map
    • H. Herzel, B. Pompe, Effects of noise on a non-uniform chaotic map, Phys. Lett. A 122 (1987) 121.
    • (1987) Phys. Lett. A , vol.122 , pp. 121
    • Herzel, H.1    Pompe, B.2
  • 104
    • 0024703013 scopus 로고
    • Chaotic behavior of an extended system
    • P.C. Hohenberg, B.I. Shraiman, Chaotic behavior of an extended system, Physica D 37 (1988) 109.
    • (1988) Physica D , vol.37 , pp. 109
    • Hohenberg, P.C.1    Shraiman, B.I.2
  • 106
    • 6244229486 scopus 로고
    • Fluctuations and scaling in a model for boundary-layer-induced turbulence
    • M.H. Jensen, Fluctuations and scaling in a model for boundary-layer- induced turbulence, Phys. Rev. Lett. 62 (1989) 1361.
    • (1989) Phys. Rev. Lett. , vol.62 , pp. 1361
    • Jensen, M.H.1
  • 107
    • 0003463010 scopus 로고    scopus 로고
    • Multiscaling and structure functions in turbulence: An alternative approach
    • M.H. Jensen, Multiscaling and structure functions in turbulence: an alternative approach, Phys. Rev. Lett. 83 (1999) 76.
    • (1999) Phys. Rev. Lett. , vol.83 , pp. 76
    • Jensen, M.H.1
  • 108
    • 0000047830 scopus 로고
    • Period-doubling of kink-antikink patterns, quasi-periodicity in antiferro-like structures and spatial intermittency in coupled map lattices-toward a prelude to a field theory of chaos
    • K. Kaneko, Period-doubling of kink-antikink patterns, quasi-periodicity in antiferro-like structures and spatial intermittency in coupled map lattices-toward a prelude to a field theory of chaos, Prog. Theor. Phys. 72 (1984) 480.
    • (1984) Prog. Theor. Phys. , vol.72 , pp. 480
    • Kaneko, K.1
  • 109
    • 45949128289 scopus 로고
    • Lyapunov analysis and information flow in coupled map lattices
    • K. Kaneko, Lyapunov analysis and information flow in coupled map lattices, Physica D 23 (1986) 436.
    • (1986) Physica D , vol.23 , pp. 436
    • Kaneko, K.1
  • 110
    • 0001586233 scopus 로고
    • Chaotic but regular posi-nega switch among coded attractors by cluster-size variation
    • K. Kaneko, Chaotic but regular posi-nega switch among coded attractors by cluster-size variation, Phys. Rev. Lett. 63 (1989) 219.
    • (1989) Phys. Rev. Lett. , vol.63 , pp. 219
    • Kaneko, K.1
  • 111
    • 5244237607 scopus 로고
    • Globally coupled chaos violates the law of large numbers but not the central-limit theorem
    • K. Kaneko, Globally coupled chaos violates the law of large numbers but not the central-limit theorem, Phys. Rev. Lett. 65 (1990) 1391.
    • (1990) Phys. Rev. Lett. , vol.65 , pp. 1391
    • Kaneko, K.1
  • 113
    • 58149211060 scopus 로고
    • Remarks on the mean field dynamics of networks of chaotic elements
    • K. Kaneko, Remarks on the mean field dynamics of networks of chaotic elements, Physica D 86 (1995) 158.
    • (1995) Physica D , vol.86 , pp. 158
    • Kaneko, K.1
  • 115
    • 10844260561 scopus 로고    scopus 로고
    • Quasi-chaos and quasi-regularity-the breakdown of linear stability analysis
    • H. Kantz, T. Letz, Quasi-chaos and quasi-regularity-the breakdown of linear stability analysis, Phys. Rev. E 61 (2000) 2533.
    • (2000) Phys. Rev. E , vol.61 , pp. 2533
    • Kantz, H.1    Letz, T.2
  • 116
    • 0033733522 scopus 로고    scopus 로고
    • Coarse grained dynamical entropies: Investigation of high entropic dynamical systems
    • H. Kantz, E. Olbrich, Coarse grained dynamical entropies: investigation of high entropic dynamical systems, Physica A 280 (2000) 34.
    • (2000) Physica A , vol.280 , pp. 34
    • Kantz, H.1    Olbrich, E.2
  • 117
    • 0002822757 scopus 로고
    • Pre turbulence: A regime observed in a fluid model of Lorenz
    • J.L. Kaplan, J.A. Yorke, Pre turbulence: a regime observed in a fluid model of Lorenz, Comm. Math. Phys. 67 (1979) 93.
    • (1979) Comm. Math. Phys. , vol.67 , pp. 93
    • Kaplan, J.L.1    Yorke, J.A.2
  • 118
    • 0002157420 scopus 로고
    • Chemical waves and coupled map lattices
    • K. Kaneko (Ed.), Wiley, New York
    • R. Kapral, Chemical waves and coupled map lattices, in: K. Kaneko (Ed.), Theory and Applications of Coupled Map Lattices, Wiley, New York, 1993, p. 135.
    • (1993) Theory and Applications of Coupled Map Lattices , pp. 135
    • Kapral, R.1
  • 119
    • 21144467355 scopus 로고
    • Dynamics of oscillations with periodic dichotomic noise
    • R. Kapral, S.J. Fraser, Dynamics of oscillations with periodic dichotomic noise, J. Stat. Phys. 70 (1993) 61.
    • (1993) J. Stat. Phys. , vol.70 , pp. 61
    • Kapral, R.1    Fraser, S.J.2
  • 122
    • 0038862540 scopus 로고
    • Error growth in a decaying two-dimensional turbulence
    • S. Kida, M. Yamada, K. Ohkitani, Error growth in a decaying two-dimensional turbulence, J. Phys. Soc. Jpn. 59 (1990) 90.
    • (1990) J. Phys. Soc. Jpn. , vol.59 , pp. 90
    • Kida, S.1    Yamada, M.2    Ohkitani, K.3
  • 123
    • 0002346018 scopus 로고
    • The local structure of turbulence in incompressible viscous fluid for very large Reynold number
    • A.N. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynold number, Dokl. Akad. Nauk. SSSR 30 (1941) 299 (reprinted in Proc. R. Soc. Lond. A 434 (1991) 9).
    • (1941) Dokl. Akad. Nauk. SSSR , vol.30 , pp. 299
    • Kolmogorov, A.N.1
  • 124
    • 0002894836 scopus 로고
    • reprinted
    • A.N. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynold number, Dokl. Akad. Nauk. SSSR 30 (1941) 299 (reprinted in Proc. R. Soc. Lond. A 434 (1991) 9).
    • (1991) Proc. R. Soc. Lond. A , vol.434 , pp. 9
  • 125
    • 77954824787 scopus 로고
    • On the Shannon theory of information transmission in the case of continuous signals
    • A.N. Kolmogorov, On the Shannon theory of information transmission in the case of continuous signals, IRE Trans. Inform. Theory 1 (1956) 102.
    • (1956) IRE Trans. Inform. Theory , vol.1 , pp. 102
    • Kolmogorov, A.N.1
  • 126
    • 0001450585 scopus 로고
    • New metric invariant of transitive dynamical systems and auto-morphism of Lebesgue spaces
    • A.N. Kolmogorov, New metric invariant of transitive dynamical systems and auto-morphism of Lebesgue spaces, Dokl. Akad. Nauk SSSR 119 (1958) 861.
    • (1958) Dokl. Akad. Nauk SSSR , vol.119 , pp. 861
    • Kolmogorov, A.N.1
  • 127
    • 0001902056 scopus 로고
    • Three approaches to the quantitative definition of information
    • A.N. Kolmogorov, Three approaches to the quantitative definition of information, Prob. Inform. Trans. 1 (1965) 1.
    • (1965) Prob. Inform. Trans. , vol.1 , pp. 1
    • Kolmogorov, A.N.1
  • 129
    • 0002722044 scopus 로고
    • Study of the diffusion equation with growth of the quantity of matter and its application to a biology problem
    • A.N. Kolmogorov, I. Petrovsky, N. Piskunov, Study of the diffusion equation with growth of the quantity of matter and its application to a biology problem, Bull. Univ. Moscow, Ser. Int. A 1 (1937) 1.
    • (1937) Bull. Univ. Moscow, Ser. Int. A , vol.1 , pp. 1
    • Kolmogorov, A.N.1    Petrovsky, I.2    Piskunov, N.3
  • 130
    • 36149035200 scopus 로고
    • Clustered motion in symplectic coupled maps system
    • T. Konishi, K. Kaneko, Clustered motion in symplectic coupled maps system, J. Phys. A 25 (1992) 6283.
    • (1992) J. Phys. A , vol.25 , pp. 6283
    • Konishi, T.1    Kaneko, K.2
  • 131
    • 0026205698 scopus 로고
    • An almost machine-independent theory of program length complexity, sophistication and induction
    • M. Koppel, H. Atlan, An almost machine-independent theory of program length complexity, sophistication and induction, Inform. Sci. 56 (1991) 23.
    • (1991) Inform. Sci. , vol.56 , pp. 23
    • Koppel, M.1    Atlan, H.2
  • 134
    • 84966257945 scopus 로고
    • On entropy and generators of measure preserving transformations
    • W. Krieger, On entropy and generators of measure preserving transformations, Trans. Am. Math. Soc. 149 (1970) 453.
    • (1970) Trans. Am. Math. Soc. , vol.149 , pp. 453
    • Krieger, W.1
  • 136
    • 84956083095 scopus 로고
    • High-resolution numerical experiments for forced two-dimensional turbulence
    • B. Legras, P. Santangelo, R. Benzi, High-resolution numerical experiments for forced two-dimensional turbulence, Europhys. Lett. 5 (1988) 37.
    • (1988) Europhys. Lett. , vol.5 , pp. 37
    • Legras, B.1    Santangelo, P.2    Benzi, R.3
  • 137
    • 0015035312 scopus 로고
    • Atmospheric predictability and two-dimensional turbulence
    • C.E. Leith, Atmospheric predictability and two-dimensional turbulence, J. Atmos. Sci. 28 (1971) 144.
    • (1971) J. Atmos. Sci. , vol.28 , pp. 144
    • Leith, C.E.1
  • 138
    • 0000282315 scopus 로고
    • Predictability of turbulent flows
    • C.E. Leith, R.H. Kraichnan, Predictability of turbulent flows, J. Atmos. Sci. 29 (1972) 1041.
    • (1972) J. Atmos. Sci. , vol.29 , pp. 1041
    • Leith, C.E.1    Kraichnan, R.H.2
  • 139
  • 140
    • 0030550740 scopus 로고    scopus 로고
    • Chronotropic Lyapunov Analysis: (I) a comprehensive characterization of 1D systems
    • S. Lepri, A. Politi, A. Torcini, Chronotropic Lyapunov Analysis: (I) a comprehensive characterization of 1D systems, J. Stat. Phys. 82 (1996) 1429.
    • (1996) J. Stat. Phys. , vol.82 , pp. 1429
    • Lepri, S.1    Politi, A.2    Torcini, A.3
  • 141
    • 0031184702 scopus 로고    scopus 로고
    • Chronotropic Lyapunov analysis: (II) towards a unified approach
    • S. Lepri, A. Politi, A. Torcini, Chronotropic Lyapunov analysis: (II) towards a unified approach, J. Stat. Phys. 88 (1997) 31.
    • (1997) J. Stat. Phys. , vol.88 , pp. 31
    • Lepri, S.1    Politi, A.2    Torcini, A.3
  • 144
    • 0343835233 scopus 로고
    • Lectures in sub-synoptic scales of motion and two-dimensional turbulence
    • P. Morel (Ed.), Riedel, Boston
    • D.K. Lilly, Lectures in sub-synoptic scales of motion and two-dimensional turbulence, in: P. Morel (Ed.), Dynamic Meteorology, Riedel, Boston, 1973.
    • (1973) Dynamic Meteorology
    • Lilly, D.K.1
  • 145
    • 0006280709 scopus 로고
    • Distribution of characteristic exponents in the thermodynamic limit
    • R. Livi, A. Politi, S. Ruffo, Distribution of characteristic exponents in the thermodynamic limit, J. Phys. A 19 (1986) 2033.
    • (1986) J. Phys. A , vol.19 , pp. 2033
    • Livi, R.1    Politi, A.2    Ruffo, S.3
  • 146
    • 0000241853 scopus 로고
    • Deterministic non-periodic flow
    • E.N. Lorenz, Deterministic non-periodic flow, J. Atmos. Sci. 20 (1963) 130.
    • (1963) J. Atmos. Sci. , vol.20 , pp. 130
    • Lorenz, E.N.1
  • 147
    • 0000853495 scopus 로고
    • The predictability of a flow which possesses many scales of motion
    • E.N. Lorenz, The predictability of a flow which possesses many scales of motion, Tellus 21 (1969) 3.
    • (1969) Tellus , vol.21 , pp. 3
    • Lorenz, E.N.1
  • 148
    • 0001846226 scopus 로고    scopus 로고
    • Predictability - A problem partly solved
    • ECMWF, Reading, 4-8 September 1995
    • E.N. Lorenz, Predictability - a problem partly solved, in: Predictability, Vol. I, Proceedings of a Seminar, ECMWF, Reading, 4-8 September 1995, 1996, p. 1.
    • (1996) Predictability, Vol. I, Proceedings of a Seminar , vol.1 , pp. 1
    • Lorenz, E.N.1
  • 149
    • 0032004313 scopus 로고    scopus 로고
    • Optimal sites for supplementary weather observations: Simulation with a small model
    • E.N. Lorenz, K.A. Emanuel, Optimal sites for supplementary weather observations: simulation with a small model, J. Atmos. Sci. 55 (1998) 399.
    • (1998) J. Atmos. Sci. , vol.55 , pp. 399
    • Lorenz, E.N.1    Emanuel, K.A.2
  • 150
    • 0000816581 scopus 로고    scopus 로고
    • On the concept of complexity for random dynamical systems
    • V. Loreto, G. Paladin, A. Vulpiani, On the concept of complexity for random dynamical systems, Phys. Rev. E 53 (1996) 2087.
    • (1996) Phys. Rev. E , vol.53 , pp. 2087
    • Loreto, V.1    Paladin, G.2    Vulpiani, A.3
  • 153
    • 0001659381 scopus 로고    scopus 로고
    • Temporal multiscaling in hydrodynamic turbulence
    • V.S. L'vov, E. Podivilov, I. Procaccia, Temporal multiscaling in hydrodynamic turbulence, Phys. Rev. E 55 (1997) 7030.
    • (1997) Phys. Rev. E , vol.55 , pp. 7030
    • L'vov, V.S.1    Podivilov, E.2    Procaccia, I.3
  • 155
    • 0016847289 scopus 로고
    • On the geometry of homogeneous turbulence, with stress on the fractal dimension of the iso-surfaces of scalars
    • B. Mandelbrot, On the geometry of homogeneous turbulence, with stress on the fractal dimension of the iso-surfaces of scalars, J. Fluid. Mech. 72 (1975) 401.
    • (1975) J. Fluid. Mech. , vol.72 , pp. 401
    • Mandelbrot, B.1
  • 156
    • 0034207252 scopus 로고    scopus 로고
    • Quantum algorithmic integrability: The metaphor of classical polygonal billiards
    • G. Mantica, Quantum algorithmic integrability: the metaphor of classical polygonal billiards, Phys. Rev. E 61 (2000) 6434.
    • (2000) Phys. Rev. E , vol.61 , pp. 6434
    • Mantica, G.1
  • 157
    • 18344371384 scopus 로고
    • The definition of random sequences
    • P. Martin-Löf, The definition of random sequences, Inform. Control 9 (1966) 602.
    • (1966) Inform. Control. , vol.9 , pp. 602
    • Martin-Löf, P.1
  • 159
    • 0038033521 scopus 로고
    • Poincare cycles, ergodicity and irreversibility in assemblies of coupled harmonic oscillators
    • P. Mazur, E. Montroll, Poincare cycles, ergodicity and irreversibility in assemblies of coupled harmonic oscillators, J. Math. Phys. 1 (1960) 70.
    • (1960) J. Math. Phys. , vol.1 , pp. 70
    • Mazur, P.1    Montroll, E.2
  • 160
    • 0021228378 scopus 로고
    • The emergence of isolated coherent vortices in turbulent shows
    • J.C. McWilliams, The emergence of isolated coherent vortices in turbulent shows, J. Fluid. Mech. 146 (1984) 21.
    • (1984) J. Fluid. Mech. , vol.146 , pp. 21
    • McWilliams, J.C.1
  • 164
    • 0002567630 scopus 로고
    • Stochastic aspects of climate transitions-response to a periodic forcing
    • C. Nicolis, Stochastic aspects of climate transitions-response to a periodic forcing, Tellus 34 (1982) 1.
    • (1982) Tellus , vol.34 , pp. 1
    • Nicolis, C.1
  • 165
    • 0000763051 scopus 로고
    • Wave number space dynamics of enstrophy cascade in a forced two-dimensional turbulence
    • K. Ohkitani, Wave number space dynamics of enstrophy cascade in a forced two-dimensional turbulence, Phys. Fluids A 3 (1991) 1598.
    • (1991) Phys. Fluids A , vol.3 , pp. 1598
    • Ohkitani, K.1
  • 166
    • 0042784516 scopus 로고    scopus 로고
    • Analyzing local observations of weakly coupled maps
    • E. Olbrich, R. Hegger, H. Kantz, Analyzing local observations of weakly coupled maps, Phys. Lett. A 244 (1998) 538.
    • (1998) Phys. Lett. A , vol.244 , pp. 538
    • Olbrich, E.1    Hegger, R.2    Kantz, H.3
  • 167
    • 0042150490 scopus 로고
    • Discrete model of chemical turbulence
    • Y. Oono, M. Kohomoto, Discrete model of chemical turbulence, Phys. Rev. Lett. 55 (1985) 2927.
    • (1985) Phys. Rev. Lett. , vol.55 , pp. 2927
    • Oono, Y.1    Kohomoto, M.2
  • 168
    • 0012953714 scopus 로고
    • A cell dynamical system model of chemical turbulence
    • Y. Oono, C. Yeung, A cell dynamical system model of chemical turbulence, J. Stat. Phys. 48 (1987) 593.
    • (1987) J. Stat. Phys. , vol.48 , pp. 593
    • Oono, Y.1    Yeung, C.2
  • 169
    • 0008425707 scopus 로고
    • Indeterminacy of the moment problem for intermittent turbulence
    • S.A. Orszag, Indeterminacy of the moment problem for intermittent turbulence, Phys. Fluids 13 (1970) 2211.
    • (1970) Phys. Fluids , vol.13 , pp. 2211
    • Orszag, S.A.1
  • 170
    • 0000543733 scopus 로고
    • A multiplicative ergodic theorem: Lyapunov characteristic numbers for dynamical systems
    • V.I. Oseledec, A multiplicative ergodic theorem: Lyapunov characteristic numbers for dynamical systems, Trans. Moscow Math. Soc. 19 (1968) 197.
    • (1968) Trans. Moscow Math. Soc. , vol.19 , pp. 197
    • Oseledec, V.I.1
  • 172
    • 4244076855 scopus 로고
    • Intermittency in chaotic systems and Renyi entropies
    • G. Paladin, A. Vulpiani, Intermittency in chaotic systems and Renyi entropies, J. Phys. A 19 (1986) 997.
    • (1986) J. Phys. A , vol.19 , pp. 997
    • Paladin, G.1    Vulpiani, A.2
  • 173
    • 45949115280 scopus 로고
    • Anomalous scaling laws in multifractal objects
    • G. Paladin, A. Vulpiani, Anomalous scaling laws in multifractal objects, Phys. Rep. 156 (1987) 147.
    • (1987) Phys. Rep. , vol.156 , pp. 147
    • Paladin, G.1    Vulpiani, A.2
  • 174
    • 36149036421 scopus 로고
    • Predictability in spatially extended systems
    • G. Paladin, A. Vulpiani, Predictability in spatially extended systems, J. Phys. A 27 (1994) 4911.
    • (1994) J. Phys. A , vol.27 , pp. 4911
    • Paladin, G.1    Vulpiani, A.2
  • 176
    • 10844226407 scopus 로고
    • Predictability of the atmoshere and oceans: From days to decades
    • ECMWF, Reading, 4-8 September
    • T.N. Palmer, Predictability of the atmoshere and oceans: from days to decades, in: Predictability, Vol. I, Proceedings of a Seminar, ECMWF, Reading, 4-8 September, 1995, p. 93.
    • (1995) Predictability, Vol. I, Proceedings of a Seminar , vol.1 , pp. 93
    • Palmer, T.N.1
  • 177
    • 0000358855 scopus 로고    scopus 로고
    • Experimental observation of the two-dimensional inverse energy cascade
    • J. Paret, P. Tabeling, Experimental Observation of the Two-Dimensional Inverse Energy Cascade, Phys. Rev. Lett. 79 (1997) 4162.
    • (1997) Phys. Rev. Lett. , vol.79 , pp. 4162
    • Paret, J.1    Tabeling, P.2
  • 178
    • 0001816154 scopus 로고
    • On the singularity structure of fully developed turbulence
    • M. Ghil et al. (Eds.), North-Holland, Amsterdam
    • G. Parisi, U. Frisch, On the singularity structure of fully developed turbulence, in: M. Ghil et al. (Eds.), Turbulence and Predictability of Geophysical Fluid Dynamics, North-Holland, Amsterdam, 1985, p. 84.
    • (1985) Turbulence and Predictability of Geophysical Fluid Dynamics , pp. 84
    • Parisi, G.1    Frisch, U.2
  • 179
    • 0000374225 scopus 로고
    • Instabilities and non-statistical behavior in globally coupled systems
    • G. Perez, H.A. Cerdeira, Instabilities and non-statistical behavior in globally coupled systems, Phys. Rev. A 46 (1992) 7492.
    • (1992) Phys. Rev. A , vol.46 , pp. 7492
    • Perez, G.1    Cerdeira, H.A.2
  • 180
    • 0000782013 scopus 로고
    • Lyapunov characteristic exponent and ergodic properties of smooth dynamical systems with an invariant measure
    • Y.B. Pesin, Lyapunov characteristic exponent and ergodic properties of smooth dynamical systems with an invariant measure, Sov. Math. Dokl. 17 (1976) 196.
    • (1976) Sov. Math. Dokl. , vol.17 , pp. 196
    • Pesin, Y.B.1
  • 181
    • 0039457010 scopus 로고
    • Spatial development of Chaos in non-linear media
    • A.S. Pikovsky, Spatial development of Chaos in non-linear media, Phys. Lett. A 137 (1989) 121.
    • (1989) Phys. Lett. A , vol.137 , pp. 121
    • Pikovsky, A.S.1
  • 182
    • 10844229251 scopus 로고
    • Does dimension grow in flow systems?
    • T. Riste, D. Sherrington (Eds.), Kluwer Academic Publishers, Dordrecht
    • A.S. Pikovsky, Does dimension grow in flow systems?, in: T. Riste, D. Sherrington (Eds.), Spontaneous formation of Space-Time Structures and Criticality, Kluwer Academic Publishers, Dordrecht, 1991.
    • (1991) Spontaneous Formation of Space-Time Structures and Criticality
    • Pikovsky, A.S.1
  • 184
    • 0001618752 scopus 로고
    • Local Lyapunov exponents for spatiotemporal chaos
    • A.S. Pikovsky, Local Lyapunov exponents for spatiotemporal chaos, Chaos 3 (1993) 225.
    • (1993) Chaos , vol.3 , pp. 225
    • Pikovsky, A.S.1
  • 185
    • 0000326536 scopus 로고
    • Collective behavior in ensembles of globally coupled maps
    • A.S. Pikovsky, J. Kurths, Collective behavior in ensembles of globally coupled maps, Physica D 76 (1994) 411.
    • (1994) Physica D , vol.76 , pp. 411
    • Pikovsky, A.S.1    Kurths, J.2
  • 186
    • 0001253793 scopus 로고
    • Roughening interfaces in the dynamics of perturbations of spatiotemporal chaos
    • A.S. Pikovsky, J. Kurths, Roughening interfaces in the dynamics of perturbations of spatiotemporal chaos, Phys. Rev. E 49 (1994) 898.
    • (1994) Phys. Rev. E , vol.49 , pp. 898
    • Pikovsky, A.S.1    Kurths, J.2
  • 187
    • 0000097505 scopus 로고    scopus 로고
    • Dynamic localization of Lyapunov vectors in space-time chaos
    • A.S. Pikovsky, A. Politi, Dynamic localization of Lyapunov vectors in space-time chaos, Nonlinearity 11 (1998) 1049.
    • (1998) Nonlinearity , vol.11 , pp. 1049
    • Pikovsky, A.S.1    Politi, A.2
  • 188
    • 12044255333 scopus 로고
    • On-off intermittency - A mechanism for bursting
    • N. Platt, E.A. Spiegel, C. Tresser, On-off intermittency - a mechanism for bursting, Phys. Rev. Lett. 70 (1993) 279.
    • (1993) Phys. Rev. Lett. , vol.70 , pp. 279
    • Platt, N.1    Spiegel, E.A.2    Tresser, C.3
  • 190
    • 0004837950 scopus 로고
    • Periodic orbits in coupled Hénon maps: Lyapunov and multifractal analysis
    • A. Politi, A. Torcini, Periodic orbits in coupled Hénon maps: Lyapunov and multifractal analysis, Chaos 2 (1992) 293.
    • (1992) Chaos , vol.2 , pp. 293
    • Politi, A.1    Torcini, A.2
  • 191
    • 84957345395 scopus 로고
    • Linear and Non-Linear mechanisms of Information propagation
    • A. Politi, A. Torcini, Linear and Non-Linear mechanisms of Information propagation, Europhys. Lett. 28 (1994) 545.
    • (1994) Europhys. Lett. , vol.28 , pp. 545
    • Politi, A.1    Torcini, A.2
  • 192
    • 34250254669 scopus 로고
    • Intermittent transition to turbulence in dissipative dynamical systems
    • Y. Pomeau, P. Mannenville, Intermittent transition to turbulence in dissipative dynamical systems, Comm. Math. Phys. 74 (1980) 189.
    • (1980) Comm. Math. Phys. , vol.74 , pp. 189
    • Pomeau, Y.1    Mannenville, P.2
  • 197
    • 33750064351 scopus 로고
    • Microscopic fluctuations and turbulence
    • D. Ruelle, Microscopic fluctuations and turbulence, Phys. Lett. A 72 (1979) 81.
    • (1979) Phys. Lett. A , vol.72 , pp. 81
    • Ruelle, D.1
  • 198
    • 0000038026 scopus 로고
    • Large volume limit of the distribution of characteristic exponents in turbulence
    • D. Ruelle, Large volume limit of the distribution of characteristic exponents in turbulence, Commun. Math. Phys. 87 (1982) 287.
    • (1982) Commun. Math. Phys. , vol.87 , pp. 287
    • Ruelle, D.1
  • 199
    • 0001617876 scopus 로고    scopus 로고
    • Unidirectionally coupled map lattices as a model for open flow systems
    • O. Rudzick, A. Pikovsky, Unidirectionally coupled map lattices as a model for open flow systems, Phys. Rev. E 54 (1996) 5107.
    • (1996) Phys. Rev. E , vol.54 , pp. 5107
    • Rudzick, O.1    Pikovsky, A.2
  • 201
    • 0000119191 scopus 로고
    • Diffusive dynamics in systems with translational symmetry-a one-dimensional-map model
    • M. Schell, S. Fraser, R. Kapral, Diffusive dynamics in systems with translational symmetry-a one-dimensional-map model, Phys. Rev. A 26 (1982) 504.
    • (1982) Phys. Rev. A , vol.26 , pp. 504
    • Schell, M.1    Fraser, S.2    Kapral, R.3
  • 203
    • 84940644968 scopus 로고
    • C.E. Shannon, A mathematical theory of communication, The Bell System Technical J. 27 (1948) 623; 27 (1948) 379.
    • (1948) The Bell System Technical J. , vol.27 , pp. 379
  • 204
    • 0031579921 scopus 로고    scopus 로고
    • Heterogeneity induced order in globally coupled systems
    • T. Shibata, K. Kaneko, Heterogeneity induced order in globally coupled systems, Europhys. Lett. 38 (1997) 417.
    • (1997) Europhys. Lett. , vol.38 , pp. 417
    • Shibata, T.1    Kaneko, K.2
  • 206
    • 0000419815 scopus 로고
    • On the concept of entropy for a dynamic system
    • Y.G. Sinai, On the concept of entropy for a dynamic system, Dokl. Akad. Nauk. SSSR 124 (1959) 768.
    • (1959) Dokl. Akad. Nauk. SSSR , vol.124 , pp. 768
    • Sinai, Y.G.1
  • 207
    • 0000344512 scopus 로고    scopus 로고
    • A remark concerning the thermodynamic limit of the Lyapunov spectrum
    • Y.G. Sinai, A remark concerning the thermodynamic limit of the Lyapunov spectrum, Int. J. Bif. Chaos 6 (1996) 1137.
    • (1996) Int. J. Bif. Chaos , vol.6 , pp. 1137
    • Sinai, Y.G.1
  • 208
    • 0001311276 scopus 로고
    • Bose condensation and small-scale structure generation in a random force driven 2D turbulence
    • L.M. Smith, V. Yakhot, Bose condensation and small-scale structure generation in a random force driven 2D turbulence, Phys. Rev. Lett. 71 (1993) 352.
    • (1993) Phys. Rev. Lett. , vol.71 , pp. 352
    • Smith, L.M.1    Yakhot, V.2
  • 209
    • 4544279425 scopus 로고
    • A formal theory of inductive inference
    • R.J. Solomonov, A formal theory of inductive inference, Inform. Control 7 (1964) 1; 7 (1964) 224.
    • (1964) Inform. Control , vol.7 , pp. 1
    • Solomonov, R.J.1
  • 210
    • 50549204079 scopus 로고
    • R.J. Solomonov, A formal theory of inductive inference, Inform. Control 7 (1964) 1; 7 (1964) 224.
    • (1964) Inform. Control , vol.7 , pp. 224
  • 211
    • 22244432425 scopus 로고
    • Experiments on 2D turbulence
    • P. Tabeling, A. Cardoso (Eds.), Plenum Press, New York
    • P. Tabeling, Experiments on 2D turbulence, in: P. Tabeling, A. Cardoso (Eds.), Turbulence a Tentative Dictionary, Plenum Press, New York, 1994, p. 13.
    • (1994) Turbulence a Tentative Dictionary , pp. 13
    • Tabeling, P.1
  • 213
    • 0005178883 scopus 로고    scopus 로고
    • Generalized entropies: Renyi and correlation integral approach
    • F. Takens, E. Verbitski, Generalized entropies: Renyi and correlation integral approach, Nonlinearity 11 (1998) 771.
    • (1998) Nonlinearity , vol.11 , pp. 771
    • Takens, F.1    Verbitski, E.2
  • 215
    • 36149031095 scopus 로고
    • Error propagation in extended chaotic systems
    • A. Torcini, P. Grassberger, A. Politi, Error propagation in extended chaotic systems, J. Phys. A 27 (1995) 4533.
    • (1995) J. Phys. A , vol.27 , pp. 4533
    • Torcini, A.1    Grassberger, P.2    Politi, A.3
  • 216
    • 0005883070 scopus 로고    scopus 로고
    • Disturbance propagation in extended systems with long range-coupling
    • A. Torcini, S. Lepri, Disturbance propagation in extended systems with long range-coupling, Phys. Rev. E 55 (1997) R3805.
    • (1997) Phys. Rev. E , vol.55
    • Torcini, A.1    Lepri, S.2
  • 217
    • 0040562586 scopus 로고    scopus 로고
    • Sensitive dependence on initial conditions for cellular automata
    • J. Urias, R. Rechtman, A. Enciso, Sensitive dependence on initial conditions for cellular automata, Chaos 7 (1997) 688.
    • (1997) Chaos , vol.7 , pp. 688
    • Urias, J.1    Rechtman, R.2    Enciso, A.3
  • 218
    • 0041389128 scopus 로고
    • Noise-induced sensitivity to the initial conditions in stochastic dynamical systems
    • C. van der Broeck, G. Nicolis, Noise-induced sensitivity to the initial conditions in stochastic dynamical systems, Phys. Rev. E 48 (1993) 4845.
    • (1993) Phys. Rev. E , vol.48 , pp. 4845
    • Van Der Broeck, C.1    Nicolis, G.2
  • 220
    • 0001278002 scopus 로고    scopus 로고
    • Spatial complex behavior in non-chaotic flow systems
    • D. Vergni, M. Falcioni, A. Vulpiani, Spatial complex behavior in non-chaotic flow systems, Phys. Rev. E 56 (1997) 6170.
    • (1997) Phys. Rev. E , vol.56 , pp. 6170
    • Vergni, D.1    Falcioni, M.2    Vulpiani, A.3
  • 221
    • 0001643045 scopus 로고
    • Random fractals: Self-affinity in noise, music, mountains and clouds
    • R.F. Voss, Random fractals: self-affinity in noise, music, mountains and clouds, Physica D 38 (1989) 362.
    • (1989) Physica D , vol.38 , pp. 362
    • Voss, R.F.1
  • 223
    • 84980078034 scopus 로고
    • The unreasonable effectiveness of mathematics in natural sciences
    • E. Wigner, The unreasonable effectiveness of mathematics in natural sciences, Comm. Pure Appl. Math. 13 (1960) 1.
    • (1960) Comm. Pure Appl. Math. , vol.13 , pp. 1
    • Wigner, E.1
  • 224
  • 225
    • 0006747191 scopus 로고
    • Origins of randomness in physical systems
    • S. Wolfram, Origins of randomness in physical systems, Phys. Rev. Lett. 55 (1985) 449.
    • (1985) Phys. Rev. Lett. , vol.55 , pp. 449
    • Wolfram, S.1
  • 227
    • 0040978657 scopus 로고
    • ε-entropy for a time series of thermal turbulence
    • X.-J. Wang, P. Gaspard, ε-entropy for a time series of thermal turbulence, Phys. Rev. A 46 (1992) R3000.
    • (1992) Phys. Rev. A , vol.46
    • Wang, X.-J.1    Gaspard, P.2
  • 228
    • 0003038217 scopus 로고
    • Algorithmic complexity of Points in Dynamical Systems
    • H. White, Algorithmic complexity of Points in Dynamical Systems, Erg. Theory Dyn. Systems 13 (1993) 807.
    • (1993) Erg. Theory Dyn. Systems , vol.13 , pp. 807
    • White, H.1
  • 229
    • 0028464716 scopus 로고
    • Bifurcations and spatial chaos in an open flow model
    • F.H. Willeboordse, K. Kaneko, Bifurcations and spatial chaos in an open flow model, Phys. Rev. Lett. 74 (1994) 533.
    • (1994) Phys. Rev. Lett. , vol.74 , pp. 533
    • Willeboordse, F.H.1    Kaneko, K.2
  • 230
    • 0000824991 scopus 로고
    • Transition to chaos for random dynamic-systems
    • L. Yu, E. Ott, Q. Chen, Transition to chaos for random dynamic-systems, Phys. Rev. Lett. 65 (1990) 2935.
    • (1990) Phys. Rev. Lett. , vol.65 , pp. 2935
    • Yu, L.1    Ott, E.2    Chen, Q.3
  • 231
    • 44949272537 scopus 로고
    • Fractal distribution of floaters on a fluid surface and the transition to chaos for random maps
    • L. Yu, E. Ott, Q. Chen, Fractal distribution of floaters on a fluid surface and the transition to chaos for random maps, Physica D 53 (1991) 102.
    • (1991) Physica D , vol.53 , pp. 102
    • Yu, L.1    Ott, E.2    Chen, Q.3
  • 232
    • 35949010691 scopus 로고
    • Scaling theory of self-organized criticality
    • Y.-C. Zhang, Scaling theory of self-organized criticality, Phys. Rev. Lett. 63 (1989) 470.
    • (1989) Phys. Rev. Lett. , vol.63 , pp. 470
    • Zhang, Y.-C.1
  • 234
    • 84949405337 scopus 로고
    • Non-uniform chaotic dynamics with implications to information processing
    • J.S. Nicolis, G. Mayer-Kress, G. Haubs, Non-uniform chaotic dynamics with implications to information processing, Z. Naturf. 38A (1983) 1157.
    • (1983) Z. Naturf. , vol.38 A , pp. 1157
    • Nicolis, J.S.1    Mayer-Kress, G.2    Haubs, G.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.