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Volumn 132, Issue 3, 1999, Pages 392-410

On the entropy devil's staircase in a family of gap-tent maps

Author keywords

Chaos communication; Devil's staircase; Fractal measure; Kneading theory; Symbol dynamics; Topological entropy

Indexed keywords


EID: 0348226529     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(99)00029-9     Document Type: Article
Times cited : (18)

References (62)
  • 15
    • 84968514104 scopus 로고
    • Differentiable Dynamical Systems
    • S. Smale, Differentiable Dynamical Systems, Bull. AMS 73 (1967) 747-817.
    • (1967) Bull. AMS , vol.73 , pp. 747-817
    • Smale, S.1
  • 21
    • 0001082245 scopus 로고    scopus 로고
    • Dynamics of coding in communicating with chaos
    • in press
    • E. Bollt, Y.-C. Lai, Dynamics of coding in communicating with chaos, Phys. Rev. E 1998, in press.
    • (1998) Phys. Rev. E
    • Bollt, E.1    Lai, Y.-C.2
  • 24
    • 0000848698 scopus 로고
    • On iterated maps of the interval Dynamical Systems
    • Springer, Berlin
    • J. Milnor, W. Thurston, On iterated maps of the interval Dynamical Systems, Lecture Notes in Math, 1342, Springer, Berlin, 1988, pp. 465-563.
    • (1988) Lecture Notes in Math , vol.1342 , pp. 465-563
    • Milnor, J.1    Thurston, W.2
  • 25
    • 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
  • 26
    • 0000207220 scopus 로고
    • Symbolic dynamics analysis of topological entropy and its multifractal structure
    • Z.-X. Chen, K.-F. Cao, S.-L. Peng, Symbolic dynamics analysis of topological entropy and its multifractal structure, Phys. Rev. E 51 (1995) 1983.
    • (1995) Phys. Rev. E , vol.51 , pp. 1983
    • Chen, Z.-X.1    Cao, K.-F.2    Peng, S.-L.3
  • 27
    • 0031582796 scopus 로고    scopus 로고
    • Structure in the parameter dependence of order and chaos for the quadratic map
    • B.R. Hunt, E. Ott, Structure in the parameter dependence of order and chaos for the quadratic map, J. Phys. A 30 (1997) 7067.
    • (1997) J. Phys. A , vol.30 , pp. 7067
    • Hunt, B.R.1    Ott, E.2
  • 28
    • 0008095926 scopus 로고
    • Universal encoding for unimodal maps
    • S. Isola, A. Politi, Universal encoding for unimodal maps, J. Stat. Phys. 61 (1990) 263.
    • (1990) J. Stat. Phys. , vol.61 , pp. 263
    • Isola, S.1    Politi, A.2
  • 29
    • 0031530948 scopus 로고    scopus 로고
    • Generic hyperbolicity in the logistic map
    • J. Graczyk, G. Świa̧tek, Generic hyperbolicity in the logistic map, Ann. Math. 146 (1997) 1.
    • (1997) Ann. Math. , vol.146 , pp. 1
    • Graczyk, J.1    Świa̧tek, G.2
  • 30
    • 84956109858 scopus 로고
    • Pressure dependence of the number of metastable configurations: A staircaselike behavior for a chain of particles
    • R. Haner, R. Schilling, Pressure dependence of the number of metastable configurations: a staircaselike behavior for a chain of particles, Europhys. Lett. 8(2) (1989) 129-134.
    • (1989) Europhys. Lett. , vol.8 , Issue.2 , pp. 129-134
    • Haner, R.1    Schilling, R.2
  • 31
    • 29444458464 scopus 로고
    • Scaling properties of a scattering system with an incomplete horseshoe
    • B. Rückerl, C. Jung, Scaling properties of a scattering system with an incomplete horseshoe, J. Phys. A: Math. Gen. 27 (1994) 55-77.
    • (1994) J. Phys. A: Math. Gen. , vol.27 , pp. 55-77
    • Rückerl, B.1    Jung, C.2
  • 32
    • 70349500072 scopus 로고
    • The isotropic-to-nematic transition in semi-flexible micellar solutions
    • P. van der Schoot, M.E. Cates, The isotropic-to-nematic transition in semi-flexible micellar solutions, Europhys. Lett. 25(7) (1994) 515-520.
    • (1994) Europhys. Lett. , vol.25 , Issue.7 , pp. 515-520
    • Van Der Schoot, P.1    Cates, M.E.2
  • 33
    • 0010465108 scopus 로고    scopus 로고
    • Symbolic dynamics and topological entropy of the onset of pruning
    • W. Breymann, J. Vollmer, Symbolic dynamics and topological entropy of the onset of pruning, Z. Phys. B 103 (1997) 539-546.
    • (1997) Z. Phys. B , vol.103 , pp. 539-546
    • Breymann, W.1    Vollmer, J.2
  • 35
    • 0000157863 scopus 로고
    • The entropy function for characteristic exponents
    • T. Bohr, D. Rand, The entropy function for characteristic exponents, Physica D 25 (1987) 387.
    • (1987) Physica D , vol.25 , pp. 387
    • Bohr, T.1    Rand, D.2
  • 36
  • 38
    • 0000621770 scopus 로고    scopus 로고
    • Calculating topological entropy for transient chaos with an application to communicating with chaos
    • J. Jacobs, E. Ott, B.R. Hunt, Calculating topological entropy for transient chaos with an application to communicating with chaos, Phys. Rev. E 57 (1998) 6577.
    • (1998) Phys. Rev. E , vol.57 , pp. 6577
    • Jacobs, J.1    Ott, E.2    Hunt, B.R.3
  • 39
    • 0347001669 scopus 로고    scopus 로고
    • Based on remarks in private correspondence with M. Misiurewicz
    • Based on remarks in private correspondence with M. Misiurewicz.
  • 44
    • 85026864455 scopus 로고
    • The growth of topological entropy for one dimensional maps, Global theory of dynamical systems
    • Springer, Berlin
    • J. Guckheimer, The growth of topological entropy for one dimensional maps, Global theory of dynamical systems, Lecture Notes in Mathematics, 819, Springer, Berlin, 1980, pp. 216-223.
    • (1980) Lecture Notes in Mathematics , vol.819 , pp. 216-223
    • Guckheimer, J.1
  • 46
    • 0005063733 scopus 로고
    • Construction of maps with generating partitions for entropy evaluation
    • C.S. Hsu, M.C. Kim, Construction of maps with generating partitions for entropy evaluation, Phys. Rev. A 31 (1985) 3253.
    • (1985) Phys. Rev. A , vol.31 , pp. 3253
    • Hsu, C.S.1    Kim, M.C.2
  • 49
    • 84966245662 scopus 로고
    • Computing the topological entropy of 1D maps
    • P. Góra, A. Boyarsky, Computing the topological entropy of 1D maps, Trans. Amer. Math. Soc. 323 (1991) 39.
    • (1991) Trans. Amer. Math. Soc. , vol.323 , pp. 39
    • Góra, P.1    Boyarsky, A.2
  • 50
    • 0002165789 scopus 로고
    • Weight-balanced measures and free energy for one-dimensional dynamics
    • A.O. Lopes, W.D. Withers, Weight-balanced measures and free energy for one-dimensional dynamics, Forum Math. 5 (1993) 161.
    • (1993) Forum Math. , vol.5 , pp. 161
    • Lopes, A.O.1    Withers, W.D.2
  • 54
    • 0000197953 scopus 로고
    • Global metric regularity of the devil's staircase of topological entropy
    • K.-F. Cao, Z.-X. Chen, S.-L. Peng, Global metric regularity of the devil's staircase of topological entropy, Phys. Rev. E 51 (1995) 1989.
    • (1995) Phys. Rev. E , vol.51 , pp. 1989
    • Cao, K.-F.1    Chen, Z.-X.2    Peng, S.-L.3
  • 56
    • 21844495389 scopus 로고
    • A nonlinear dynamics interpretation of algorithmic A/C conversion
    • M.P. Kennedy, A nonlinear dynamics interpretation of algorithmic A/C conversion, Int. J. Bifurcation and Chaos 5 (1995) 891.
    • (1995) Int. J. Bifurcation and Chaos , vol.5 , pp. 891
    • Kennedy, M.P.1
  • 59
    • 0000230370 scopus 로고
    • Invariant measures for Markov processes arising from iterated function systems with place-dependent probabilities
    • M.F. Barnsley, S.G. Demko, J.H. Elton, J.S. Geronimo, Invariant measures for Markov processes arising from iterated function systems with place-dependent probabilities, Ann. Inst. Henri Poincaré 24 (1988) 367.
    • (1988) Ann. Inst. Henri Poincaré , vol.24 , pp. 367
    • Barnsley, M.F.1    Demko, S.G.2    Elton, J.H.3    Geronimo, J.S.4
  • 60
    • 0347632571 scopus 로고    scopus 로고
    • M.F. Barnsley, S.G. Demko, J.H. Elton, J.S. Geronimo, Erratum, 25 (1989) 589
    • M.F. Barnsley, S.G. Demko, J.H. Elton, J.S. Geronimo, Erratum, 25 (1989) 589.
  • 61
    • 21844498754 scopus 로고
    • Iterated function systems and dynamical systems
    • P.G óra, A. Boyarsky, Iterated function systems and dynamical systems. Chaos 5 (1995) 1.
    • (1995) Chaos , vol.5 , pp. 1
    • Góra, P.1    Boyarsky, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.