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Volumn , Issue , 2008, Pages 1-4448

Global transversality, resonance and chaotic dynamics

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EID: 84967560750     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/6584     Document Type: Book
Times cited : (68)

References (114)
  • 1
    • 0001333910 scopus 로고
    • Self-similarity of stochastic magnetic field lines near the X-point
    • Abdullaev, S.S. and Zaslavsky, G.M., 1995, Self-similarity of stochastic magnetic field lines near the X-point, Physics of Plasmas, 2,4533-4541.
    • (1995) Physics of Plasmas , vol.2 , pp. 4533-4541
    • Abdullaev, S.S.1    Zaslavsky, G.M.2
  • 2
    • 0000667843 scopus 로고    scopus 로고
    • Application of the separatrix map to study perturbed magnetic field lines near the separatrix
    • Abdullaev, S.S. and Zaslavsky, G.M., 1996, Application of the separatrix map to study perturbed magnetic field lines near the separatrix, Physics of Plasmas, 3, 516-528.
    • (1996) Physics of Plasmas , vol.3 , pp. 516-528
    • Abdullaev, S.S.1    Zaslavsky, G.M.2
  • 3
    • 22244451042 scopus 로고    scopus 로고
    • Analysis of the separatrix map in Hamiltonian systems
    • Ahn, T., Kim, G. and Kim, S., 1996, Analysis of the separatrix map in Hamiltonian systems, Physica D, 89, 3 15-328.
    • (1996) Physica D , vol.89 , Issue.3 , pp. 15-328
    • Ahn, T.1    Kim, G.2    Kim, S.3
  • 5
    • 0742288604 scopus 로고    scopus 로고
    • Potential in stochastic differential equations: Novel construction
    • Ao, P., 2004, Potential in stochastic differential equations: Novel construction, Journal of Physics A: Mathematical and General, 37, L25-L30.
    • (2004) Journal of Physics A: Mathematical and General , vol.37 , pp. L25-L30
    • Ao, P.1
  • 6
    • 20344364613 scopus 로고    scopus 로고
    • Laws in Darwinian Evolutionary Theory
    • Ao, P., 2005, Laws in Darwinian Evolutionary Theory, Physics of Life Reviews, 2(2), 117-156.
    • (2005) Physics of Life Reviews , vol.2 , Issue.2 , pp. 117-156
    • Ao, P.1
  • 7
    • 0002356196 scopus 로고
    • Small denominators and the problem of stability of motion in classical and celestial mechanics
    • Arnold, V.I., 1963, Small denominators and the problem of stability of motion in classical and celestial mechanics, Russian Mathematical Surveys, 18
    • (1963) Russian Mathematical Surveys , pp. 18
    • Arnold, V.I.1
  • 8
    • 0000877933 scopus 로고
    • Instability of dynamical systems with several degrees of freedom
    • Arnold, V.I., 1964, Instability of dynamical systems with several degrees of freedom, Soviet Mathematics Doklody, 5, 58 1-585.
    • (1964) Soviet Mathematics Doklody , vol.5 , Issue.58 , pp. 1-585
    • Arnold, V.I.1
  • 10
    • 4644344942 scopus 로고    scopus 로고
    • Ph.D. thesis, Department of Aerospace Engineering, the University of Cincinnati, Cincinnati, Ohio, USA
    • Bartler, T., 1999, Lyapunov Exponents and Chaos Investigation, Ph.D. thesis, Department of Aerospace Engineering, the University of Cincinnati, Cincinnati, Ohio, USA.
    • (1999) Lyapunov Exponents and Chaos Investigation
    • Bartler, T.1
  • 11
    • 35949037738 scopus 로고
    • Kolmogorov entropy and numerical experiments
    • Benettin, G., Galgani, L. and Strelcyn, J.M., 1976, Kolmogorov entropy and numerical experiments, Physical Review, A14, 2338-2345.
    • (1976) Physical Review , vol.A14 , pp. 2338-2345
    • Benettin, G.1    Galgani, L.2    Strelcyn, J.M.3
  • 12
    • 0018989294 scopus 로고
    • Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems: A method for computing all of them-1.Theory
    • Benettin, G., Galgani, L., Giorgilli, A. and Strelcyn, J.M., 1980a, Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems: a method for computing all of them-1.Theory, Meccanica, 15, 9-2 1
    • (1980) Meccanica , vol.15 , Issue.2-9 , pp. 1
    • Benettin, G.1    Galgani, L.2    Giorgilli, A.3    Strelcyn, J.M.4
  • 13
    • 0018989294 scopus 로고
    • Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems: A method for computing all of them-2. Numerical Applications
    • Benettin, G., Galgani, L., Giorgilli, A. and Strelcyn, J.M., 1980b, Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems: a method for computing all of them-2. Numerical Applications, Meccanica, 15,9-21
    • (1980) Meccanica , vol.15 , pp. 9-21
    • Benettin, G.1    Galgani, L.2    Giorgilli, A.3    Strelcyn, J.M.4
  • 16
    • 27144440687 scopus 로고
    • Resonance processes in magnetic traps, JournaI of Nuclear Energy
    • Chirikov, B.V., 1960, Resonance processes in magnetic traps, JournaI of Nuclear Energy, Part C Plasma, 1,253-260.
    • (1960) Part C Plasma , vol.1 , pp. 253-260
    • Chirikov, B.V.1
  • 17
    • 0012097571 scopus 로고
    • A universal instability of many-dimensional oscillator systems
    • Chirikov, B.V., 1979, A universal instability of many-dimensional oscillator systems, Physics Reports, 52,263-379.
    • (1979) Physics Reports , vol.52 , pp. 263-379
    • Chirikov, B.V.1
  • 18
    • 0028374128 scopus 로고
    • Unitary integrators and application to continuous orthogonalization techniques
    • Dieci, L., Russell, R. and Velk, E.V., 1994, Unitary integrators and application to continuous orthogonalization techniques, SIAM Journal of Numerical Analysis, 31,261-281.
    • (1994) SIAM Journal of Numerical Analysis , vol.31 , pp. 261-281
    • Dieci, L.1    Russell, R.2    Velk, E.V.3
  • 19
    • 84967494294 scopus 로고
    • Computation of a few Lyapunov exponents for continuous and discrete dynamical systems
    • Dieci, L.and Velk, E.V., 1995, Computation of a few Lyapunov exponents for continuous and discrete dynamical systems, Applied Numerical Mathematics, 34,403-423.
    • (1995) Applied Numerical Mathematics , vol.34 , pp. 403-423
    • Dieci, L.1
  • 20
    • 0000223905 scopus 로고    scopus 로고
    • On the computation of Lyapunov exponents for continuous dynamical systems
    • Dieci, L., Russell, R. and Velk, E.V., 1997, On the computation of Lyapunov exponents for continuous dynamical systems, SIAM Journal of Numerical Analysis, 34,403-423.
    • (1997) SIAM Journal of Numerical Analysis , vol.34 , pp. 403-423
    • Dieci, L.1    Russell, R.2    Velk, E.V.3
  • 21
    • 0000591957 scopus 로고
    • Renormalization method for the onset of stochasticity in a Hamiltonian system
    • Escande, D.F. and Doveil, F., 1981, Renormalization method for the onset of stochasticity in a Hamiltonian system. Physical Letter, 83A, 307-3 10.
    • (1981) Physical Letter , vol.83 A
    • Escande, D.F.1    Doveil, F.2
  • 22
    • 0000694866 scopus 로고
    • Stochasticity in classic Hamiltonian systems: Universal aspects
    • Escande, D.F., 1985, Stochasticity in classic Hamiltonian systems: universal aspects, Physics Reports, 121, 165-261.
    • (1985) Physics Reports , vol.121 , pp. 165-261
    • Escande, D.F.1
  • 23
    • 0026413023 scopus 로고
    • Hamiltonian algorithms for Hamiltonian systems and a comparative numerical study
    • Feng, K. and Qin, M.Z., 1991, Hamiltonian algorithms for Hamiltonian systems and a comparative numerical study, Computer Physics Communications, 65, 173-187.
    • (1991) Computer Physics Communications , vol.65 , pp. 173-187
    • Feng, K.1    Qin, M.Z.2
  • 24
    • 0001409346 scopus 로고
    • Destruction of magnetic surfaces by magnetic field irregularities: Part 11
    • Filonenko, N.N., Sagdeev, R.Z. and Zaslavsky, G.M., 1967, Destruction of magnetic surfaces by magnetic field irregularities: Part 11, Nuclear Fusion, 7,253-266.
    • (1967) Nuclear Fusion , vol.7 , pp. 253-266
    • Filonenko, N.N.1    Sagdeev, R.Z.2    Zaslavsky, G.M.3
  • 26
    • 0001327147 scopus 로고
    • Exponentially small splitting in Hamiltonian systems
    • Gelfieich, V.G., Lazutkin, V.F. and Tabanov, M.B., 1991, Exponentially small splitting in Hamiltonian systems, Chaos, 1, 137-142.
    • (1991) Chaos , vol.1 , pp. 137-142
    • Gelfieich, V.G.1    Lazutkin, V.F.2    Tabanov, M.B.3
  • 27
    • 0002439526 scopus 로고
    • A refined formula for the separatrix splitting for the standard map
    • Gelfieich, V.G., Lazutkin, V.F. and Svanidze, N.V., 1994, A refined formula for the separatrix splitting for the standard map, Physica D, 71, 82-101.
    • (1994) Physica D , vol.71 , pp. 82-101
    • Gelfieich, V.G.1    Lazutkin, V.F.2    Svanidze, N.V.3
  • 29
    • 0007091042 scopus 로고
    • Stability and Lyapunov stability of dynamical system: A differential approach and a numerical method
    • Goldhirsch, I., Sulem, P. and Orszag, S., 1987, Stability and Lyapunov stability of dynamical system: a differential approach and a numerical method, Physica D, 27,3 11-337.
    • (1987) Physica D , vol.27 , Issue.3 , pp. 11-337
    • Goldhirsch, I.1    Sulem, P.2    Orszag, S.3
  • 31
    • 36849114757 scopus 로고
    • Two-dimensional measure-preserving mappings
    • Greene, J.M., 1968, Two-dimensional measure-preserving mappings, Journal of Mathematical Physics, 9,760-768.
    • (1968) Journal of Mathematical Physics , vol.9 , pp. 760-768
    • Greene, J.M.1
  • 32
    • 84967639629 scopus 로고
    • A method for computing the stochastic transition
    • Greene, J.M., 1979, A method for computing the stochastic transition, Journal of Mathematical Physics, 20, 11 83-1201.
    • (1979) Journal of Mathematical Physics , vol.20 , Issue.11 , pp. 83-1201
    • Greene, J.M.1
  • 33
    • 33748303912 scopus 로고
    • Bifurcations in periodically forced oscillations: Subharmonics and homoclinic orbits
    • Cornell University, USA
    • Greenspan, B.D., 1981, Bifurcations in periodically forced oscillations: subharmonics and homoclinic orbits, Ph. D. thesis, Center for Applied Mathematics, Cornell University, USA.
    • (1981) Ph.D. thesis, Center for Applied Mathematics
    • Greenspan, B.D.1
  • 34
    • 0001991757 scopus 로고
    • Homoclinic orbits, subharmonics and global bifurcations in forced oscillations
    • G.Barenblatt, G. Iooss, and D.D. Joseph (eds.) London, Pitman
    • Greenspan, B.D. and Holmes, P.J., 1983, Homoclinic orbits, subharmonics and global bifurcations in forced oscillations, In Nonlinear Dynamics and Turbulence, G.Barenblatt, G. Iooss, and D.D. Joseph (eds.) London, Pitman.
    • (1983) Nonlinear Dynamics and Turbulence
    • Greenspan, B.D.1    Holmes, P.J.2
  • 38
    • 0002519122 scopus 로고
    • The applicability of the third integral motion: Some numerical experiments
    • Henon, M. and Heiles, C., 1964, The applicability of the third integral motion: Some numerical experiments, Astronomical Journal, 69,73-79.
    • (1964) Astronomical Journal , vol.69 , pp. 73-79
    • Henon, M.1    Heiles, C.2
  • 39
    • 0004251104 scopus 로고
    • Ergebnisse der Mathematics und ihrer Grenzgebiete Springer: Berlin
    • Hopf, E., 1937, Ergodentheorie, Ergebnisse der Mathematics und ihrer Grenzgebiete, Springer: Berlin.
    • (1937) Ergodentheorie
    • Hopf, E.1
  • 40
    • 0000255261 scopus 로고
    • Exponentially small splitthgs of separatrices with applications to KAM theory and degenerate bifurcations
    • Holmes, P.J., Marsden, J.E. and Scheurle, J.,1988, Exponentially small splitthgs of separatrices with applications to KAM theory and degenerate bifurcations, Contemporary Mathematics, 81,2 13-244.
    • (1988) Contemporary Mathematics , vol.81 , Issue.2 , pp. 13-244
    • Holmes, P.J.1    Marsden, J.E.2    Scheurle, J.3
  • 41
    • 0002993688 scopus 로고    scopus 로고
    • Semiclassical quantization of a separatrix map
    • Iomin, A. and Fishman, S., 1996, Semiclassical quantization of a separatrix map, Physical Review E, 54, Rl-R5.
    • (1996) Physical Review E , vol.54 , pp. Rl-R5
    • Iomin, A.1    Fishman, S.2
  • 43
    • 0001246972 scopus 로고
    • The conservation of conditionally periodic motions under a small perturbations of the Hamiltonian
    • Kolmogorov, A.N., 1954, The conservation of conditionally periodic motions under a small perturbations of the Hamiltonian, Doklady Akademy Nauk SSSR, 98,527-530.
    • (1954) Doklady Akademy Nauk SSSR , vol.98 , pp. 527-530
    • Kolmogorov, A.N.1
  • 44
  • 46
    • 0024926295 scopus 로고
    • Splitting of separatrices for standard and semistandard mappings
    • Lazutkin, V.F., Schachmannski, I.G. and Tabanov, M.B., 1989, Splitting of separatrices for standard and semistandard mappings, Physica D, 40, 235-248.
    • (1989) Physica D , vol.40 , pp. 235-248
    • Lazutkin, V.F.1    Schachmannski, I.G.2    Tabanov, M.B.3
  • 49
    • 0000541302 scopus 로고
    • External field induced chaos in an infinite square well potential
    • Lin, W.A. and Reichl, L.E., 1986, External field induced chaos in an infinite square well potential, Physica D, 19, 145-152.
    • (1986) Physica D , vol.19 , pp. 145-152
    • Lin, W.A.1    Reichl, L.E.2
  • 51
    • 9544238117 scopus 로고    scopus 로고
    • Computing Lyapunov exponents of continuous dynamical systems: Method of Lyapunov vectors
    • Lu, J., Yang, G., Oh, H. and Luo, A.C.J., 2005, Computing Lyapunov exponents of continuous dynamical systems: Method of Lyapunov vectors, Chaos, Solitons and Fractals, 23, 1879-1892.
    • (2005) Chaos, Solitons and Fractals , vol.23 , pp. 1879-1892
    • Lu, J.1    Yang, G.2    Oh, H.3    Luo, A.C.J.4
  • 52
    • 0003845853 scopus 로고
    • Analytical modeling of bifurcations, chaos and multifractals in nonlinear dynamics
    • University of Manitoba, Winnipeg, Manitoba, Canada
    • Luo, A.C.J., 1995, Analytical modeling of bifurcations, chaos and multifractals in nonlinear dynamics. Ph. D. Dissertation, University of Manitoba, Winnipeg, Manitoba, Canada.
    • (1995) Ph. D. Dissertation
    • Luo, A.C.J.1
  • 53
    • 0035825915 scopus 로고    scopus 로고
    • Resonant-overlap phenomena in stochastic layers of nonlinear Hamiltonian systems with periodical excitations
    • Luo, A.C.J., 2001a, Resonant-overlap phenomena in stochastic layers of nonlinear Hamiltonian systems with periodical excitations, Journal of Sound and Vibration, 240(5), 821-836.
    • (2001) Journal of Sound and Vibration , vol.240 , Issue.5 , pp. 821-836
    • Luo, A.C.J.1
  • 54
    • 0035435273 scopus 로고    scopus 로고
    • Resonance and stochastic layer in a parametrically excited pendulum
    • Luo, A.C.J., 2001b, Resonance and stochastic layer in a parametrically excited pendulum, Nonlinear Dynamics, 26,355-367.
    • (2001) Nonlinear Dynamics , vol.26 , pp. 355-367
    • Luo, A.C.J.1
  • 55
    • 0035969449 scopus 로고    scopus 로고
    • Chaotic motions in the generic separatrix band of the Mathieu-Duffmg oscillator
    • Luo, A.C.J., 2001c, Chaotic motions in the generic separatrix band of the Mathieu-Duffmg oscillator, Journal of Sound and Vibration, 248(3), 52 1 -532.
    • (2001) Journal of Sound and Vibration , vol.248 , Issue.3
    • Luo, A.C.J.1
  • 57
    • 19944414972 scopus 로고    scopus 로고
    • Nonlinear Dynamics theory of stochastic layers in nonlinear Hamiltonian
    • Luo, A.C.J., 2004a, Nonlinear Dynamics theory of stochastic layers in nonlinear Hamiltonian, Applied Mechanics Review, 57, 16 1 -172.
    • (2004) Applied Mechanics Review , vol.57 , Issue.16 , pp. 1-172
    • Luo, A.C.J.1
  • 58
    • 2542471713 scopus 로고    scopus 로고
    • Chaotic motion in the resonant separatrix bands of a Mathieu-Duffing oscillator with a Twin-well Potential
    • Luo, A.C.J., 2004b, Chaotic motion in the resonant separatrix bands of a Mathieu-Duffing oscillator with a Twin-well Potential, Journal of Sound and Vibrations, 273,653-666.
    • (2004) Journal of Sound and Vibrations , vol.273 , pp. 653-666
    • Luo, A.C.J.1
  • 60
    • 27544491254 scopus 로고    scopus 로고
    • Chaotic motions in traveling plates, IMeCHe, Part K
    • Luo, A.C.J., 2005b, Chaotic motions in traveling plates, IMeCHe, Part K, Journal of Multi-body Dynamics, 219,237-247.
    • (2005) Journal of Multi-body Dynamics , vol.219 , pp. 237-247
    • Luo, A.C.J.1
  • 61
    • 18544369896 scopus 로고    scopus 로고
    • Imaginary, sink and source flows in the vicinity of separatrix of non-smooth dynamical systems
    • Luo, A.C.J., 2005c, Imaginary, sink and source flows in the vicinity of separatrix of non-smooth dynamical systems, Journal of Sound and Vibration 285,443-456.
    • (2005) Journal of Sound and Vibration , vol.285 , pp. 443-456
    • Luo, A.C.J.1
  • 62
    • 27644497275 scopus 로고    scopus 로고
    • Predictions of quasi-periodic and chaotic motions in nonlinear Hamiltonian systems, Chaos
    • Luo, A.C.J., 2006a, Predictions of quasi-periodic and chaotic motions in nonlinear Hamiltonian systems, Chaos, Solitons and Fractals 28, 627-649.
    • (2006) Solitons and Fractals , vol.28 , pp. 627-649
    • Luo, A.C.J.1
  • 64
    • 44649107049 scopus 로고    scopus 로고
    • Chaos and quasi-periodic motion on the separatrix surface in nonlinear Hamiltonian system
    • Luo, A.C.J., 2006c, Chaos and quasi-periodic motion on the separatrix surface in nonlinear Hamiltonian system, ASME Journal of Computational and Nonlinear Dynamics, 1, 135-142.
    • (2006) ASME Journal of Computational and Nonlinear Dynamics , vol.1 , pp. 135-142
    • Luo, A.C.J.1
  • 65
    • 33744546851 scopus 로고    scopus 로고
    • On grazing and strange attractor fragmentation in nonsmooth dynamical systems
    • Luo, A.C.J., 2006d, On grazing and strange attractor fragmentation in nonsmooth dynamical systems, Communications in Nonlinear Science and Numerical Simulation 11,922-933.
    • (2006) Communications in Nonlinear Science and Numerical Simulation , vol.11 , pp. 922-933
    • Luo, A.C.J.1
  • 66
  • 67
    • 34347360568 scopus 로고    scopus 로고
    • On global transversality and chaos in two-dimensional dynamical systems
    • Luo, A.C.J. 2007b, On global transversality and chaos in two-dimensional dynamical systems, ASME Journal of Computational and Nonlinear Dynamics, 2,242-248.
    • (2007) ASME Journal of Computational and Nonlinear Dynamics , vol.2 , pp. 242-248
    • Luo, A.C.J.1
  • 68
    • 84967508594 scopus 로고    scopus 로고
    • Global tangency and transversality of periodic flows and chaos in a periodically forced, damped Duffmg oscillator
    • press
    • Luo, A.C.J., 2007c, Global tangency and transversality of periodic flows and chaos in a periodically forced, damped Duffmg oscillator, International Journal of Bifurcations and Chaos, in press.
    • (2007) International Journal of Bifurcations and Chaos
    • Luo, A.C.J.1
  • 70
    • 0037289962 scopus 로고    scopus 로고
    • On Resonant separatrix bands of a Duffmg oscillator with twin-well potentials, Chaos
    • Luo, A.C.J. and Gu, K., 2003, On Resonant separatrix bands of a Duffmg oscillator with twin-well potentials, Chaos, Solitons and Fractals, 15, 771-782.
    • (2003) Solitons and Fractals , vol.15 , pp. 771-782
    • Luo, A.C.J.1    Gu, K.2
  • 71
    • 0032668353 scopus 로고    scopus 로고
    • Resonant-separatrix webs in stochastic layers of the twin-well Duffig oscillator
    • Luo, A.C.J., Gu, K. and Han, R.P.S., 1999, Resonant-separatrix webs in stochastic layers of the twin-well Duffig oscillator, Nonlinear Dynamics, 19
    • (1999) Nonlinear Dynamics , pp. 19
    • Luo, A.C.J.1    Gu, K.2    Han, R.P.S.3
  • 72
    • 0001642259 scopus 로고    scopus 로고
    • Analytical predictions of chaos in a nonlinear rod
    • Luo, A.C.J. and Han, R.P.S., 1999, Analytical predictions of chaos in a nonlinear rod, Journal of Sound and Vibration, 227 (3), 523-544.
    • (1999) Journal of Sound and Vibration , vol.227 , Issue.3 , pp. 523-544
    • Luo, A.C.J.1    Han, R.P.S.2
  • 73
    • 0033721122 scopus 로고    scopus 로고
    • Investigations of stochastic layers in nonlinear dynamics
    • Luo, A.C.J. and Han, R.P.S., 2000a, Investigations of stochastic layers in nonlinear dynamics, Journal of Vibration and Acoustics, 122,36-4 1.
    • (2000) Journal of Vibration and Acoustics , vol.122
    • Luo, A.C.J.1    Han, R.P.S.2
  • 74
    • 0034326033 scopus 로고    scopus 로고
    • The dynamics of resonant and stochastic layers in a periodically-driven pendulum, Chaos
    • Luo, A.C.J. and Han, R.P.S., 2000b, The dynamics of resonant and stochastic layers in a periodically-driven pendulum, Chaos, Solitons and Frac-tals, 11,2349-2359.
    • (2000) Solitons and Frac-tals , vol.11 , pp. 2349-2359
    • Luo, A.C.J.1    Han, R.P.S.2
  • 75
    • 0035480463 scopus 로고    scopus 로고
    • The resonance theory for stochastic layers in nonlinear dynamical systems, Chaos
    • Luo, A.C.J. and Han, R.P.S.,2001, The resonance theory for stochastic layers in nonlinear dynamical systems, Chaos, Solitons and Fractals, 12, 2493-2508.
    • (2001) Solitons and Fractals , vol.12 , pp. 2493-2508
    • Luo, A.C.J.1    Han, R.P.S.2
  • 76
    • 0029206445 scopus 로고
    • Chaotic analysis of subharmonic resonant waves in undamped and damped strings
    • Luo, A.C.J., Han, R.P.S. and Xiang, Y.M., 1995, Chaotic analysis of subharmonic resonant waves in undamped and damped strings, Journal of Hydrodynamics, 7B, 92-104.
    • (1995) Journal of Hydrodynamics , vol.7 B , pp. 92-104
    • Luo, A.C.J.1    Han, R.P.S.2    Xiang, Y.M.3
  • 77
    • 1342337622 scopus 로고    scopus 로고
    • Chaotic motion in a micro-electro-mechanical system with non-linearity from capacitors
    • Luo, A.C.J. and Wang, F.Y., 2002, Chaotic motion in a micro-electro-mechanical system with non-linearity from capacitors, Communications in Nonlinear Science and Numerical Simulation, 7, 3 1-49.
    • (2002) Communications in Nonlinear Science and Numerical Simulation , vol.7 , Issue.3 , pp. 1-49
    • Luo, A.C.J.1    Wang, F.Y.2
  • 78
    • 3943078617 scopus 로고    scopus 로고
    • Nonlinear dynamics of a micro-electromechanical system with time-varying capacitors
    • Luo, A.C.J. and Wang, F.Y., 2004, Nonlinear dynamics of a micro-electromechanical system with time-varying capacitors, ASME Journal of Vibration anddcoustics, 126,77-83.
    • (2004) ASME Journal of Vibration anddcoustics , vol.126 , pp. 77-83
    • Luo, A.C.J.1    Wang, F.Y.2
  • 79
    • 0001525304 scopus 로고
    • The general problem of the stability of motion
    • Translation from Russian to French in ‘Probleme general de la stabilite du mouvement’, Annual Fac. Sci. Toulouse, reprinted in Annals Mathematical Studies 17, Princeton University Press
    • Lyapunov, A.M., 1907, The general problem of the stability of motion. Communications in Society of Mathematics Kharkov. Translation from Russian to French in ‘Probleme general de la stabilite du mouvement’, Annual Fac. Sci. Toulouse (2), 9, 203-475 reprinted in Annals Mathematical Studies 17, Princeton University Press, 1947.
    • (1907) Communications in Society of Mathematics Kharkov , vol.9 , Issue.2 , pp. 203-475
    • Lyapunov, A.M.1
  • 80
    • 0346653215 scopus 로고
    • The accuracy of symplectic integrators
    • McLachlan, R. and Atela, P., 1992, The accuracy of symplectic integrators, Nonlinearity, 5, 54 1-562.
    • (1992) Nonlinearity , vol.5 , Issue.54 , pp. 1-562
    • McLachlan, R.1    Atela, P.2
  • 81
    • 0001505841 scopus 로고
    • On the behavior of trajectories of system near to autonomous Hamiltonian systems
    • Melnikov, V.K., 1962, On the behavior of trajectories of system near to autonomous Hamiltonian systems, Soviet Mathematics-Doklady, 3, 109-1 12.
    • (1962) Soviet Mathematics-Doklady , vol.3
    • Melnikov, V.K.1
  • 82
    • 0001834849 scopus 로고
    • On the stability of the center for time periodic perturbations
    • Melnikov, V.K., 1963, On the stability of the center for time periodic perturbations, Transaction Moscow Mathematical Society, 12, 1-57.
    • (1963) Transaction Moscow Mathematical Society , vol.12 , pp. 1-57
    • Melnikov, V.K.1
  • 84
    • 0001851184 scopus 로고
    • On the invariant curves of area-preserving mapping on an annulus, Nachr
    • Moser, J., 1962, On the invariant curves of area-preserving mapping on an annulus, Nachr, Akad. Wiss. Goettingen Math. Phys. KI., 1, l-20.
    • (1962) Akad. Wiss. Goettingen Math. Phys. KI , vol.1 , pp. 1-20
    • Moser, J.1
  • 85
    • 0021660205 scopus 로고
    • The separation of motion in systems with rapidly rotating phase,(PMM)
    • Neishtadt, A.I., 1984, The separation of motion in systems with rapidly rotating phase,(PMM) Journal of Applied Mathematics and Mechanics, 48, 133-139.
    • (1984) Journal of Applied Mathematics and Mechanics , vol.48 , pp. 133-139
    • Neishtadt, A.I.1
  • 86
    • 84908024292 scopus 로고
    • An exponential estimate of the time of stability of nearly-integrable Hamiltonian systems
    • Nekhoroshev, N.N., 1977, An exponential estimate of the time of stability of nearly-integrable Hamiltonian systems, Russian Mathematics Surveys,32(6), 1-65.
    • (1977) Russian Mathematics Surveys , vol.32 , Issue.6 , pp. 1-65
    • Nekhoroshev, N.N.1
  • 87
    • 77951516344 scopus 로고
    • Sur La Probleme des Trois Corps et les Equations de la Dynamique
    • Pohcare, H., 1890, Sur La Probleme des Trois Corps et les Equations de la Dynamique, Acta Mathematica, 13, l-27
    • (1890) Acta Mathematica , vol.13 , pp. 1-27
    • Pohcare, H.1
  • 90
    • 0000232707 scopus 로고
    • Field-Induced barrier penetration in the quadratic potential
    • Reichl, L.E. and Zheng, W.M., 1984a, Field-Induced barrier penetration in the quadratic potential, Physical Review, 29A, 2 186-2 193.
    • (1984) Physical Review , vol.29 A , Issue.2
    • Reichl, L.E.1    Zheng, W.M.2
  • 91
    • 5344281002 scopus 로고
    • Perturbed double-well system: The pendulum approximation and low-frequency effect
    • Reichl, L.E. and Zheng, W.M., 1984b, Perturbed double-well system: The pendulum approximation and low-frequency effect, Physical Review, 30A, 1068-1077.
    • (1984) Physical Review , vol.30 A , pp. 1068-1077
    • Reichl, L.E.1    Zheng, W.M.2
  • 92
    • 0001301218 scopus 로고
    • Transport rates of a class of two-dimensional maps
    • Rom-Kedar, V., 1990, Transport rates of a class of two-dimensional maps Physica D, 43,229-268
    • (1990) Physica D , vol.43 , pp. 229-268
    • Rom-Kedar, V.1
  • 93
    • 10044277502 scopus 로고
    • Homoclinic tangles-classification and applications
    • Rom-Kedar, V., 1994, Homoclinic tangles-classification and applications, Nonlinearity, 7,44 1-473.
    • (1994) Nonlinearity , vol.7 , Issue.44 , pp. 1-473
    • Rom-Kedar, V.1
  • 97
    • 0004682875 scopus 로고
    • Motion of a one-dimensional nonlinear oscillator under adiabatic conditions
    • Slutskin, A. A., 1964, Motion of a one-dimensional nonlinear oscillator under adiabatic conditions, Soviet Physics JETP, 18, 676-682.
    • (1964) Soviet Physics JETP , vol.18 , pp. 676-682
    • Slutskin, A.A.1
  • 98
    • 84968514104 scopus 로고
    • Differentiable Dynamical Systems. Bull
    • Smale, S., 1967, Differentiable Dynamical Systems. Bull. American Mathematical Society, 73, 747-8 17.
    • (1967) American Mathematical Society , vol.73
    • Smale, S.1
  • 102
    • 0001933704 scopus 로고    scopus 로고
    • Width of stochastic layers in near-integrable two-dimensional symplectic maps
    • Treschev, D.V., 1998, Width of stochastic layers in near-integrable two-dimensional symplectic maps, Physica D, 116,21-43.
    • (1998) Physica D , vol.116 , pp. 21-43
    • Treschev, D.V.1
  • 103
    • 21344459207 scopus 로고    scopus 로고
    • Motion in the vicinity of the separatrix of a nonlinear resonance in the presence of high-frequency excitations
    • Vecheslavov, V.V., 1996, Motion in the vicinity of the separatrix of a nonlinear resonance in the presence of high-frequency excitations, Soviet Physi-cs JEPT, 82, 1190-1 195.
    • (1996) Soviet Physi-cs JEPT , vol.82
    • Vecheslavov, V.V.1
  • 104
    • 0035876984 scopus 로고    scopus 로고
    • An efficient and stable approach for computation of Lyapunov characteristic exponents of continuous dynamical systems
    • Udwadia, F. and Von Bremen, H., 2001, An efficient and stable approach for computation of Lyapunov characteristic exponents of continuous dynamical systems, Applied Mathematical Computation, 121,2 19-58.
    • (2001) Applied Mathematical Computation , vol.121 , Issue.2 , pp. 19-58
    • Udwadia, F.1    Von Bremen, H.2
  • 105
    • 0001804640 scopus 로고
    • Steady motions exhibited by Duffmg’s equation: A picture book of regular and chaotic motion
    • P.J. Holmes (ed.) SIAM, Philadelphia, PA
    • Ueda, Y., 1980, Steady motions exhibited by Duffmg’s equation: A picture book of regular and chaotic motion, In New Approaches to Nonlinear Problems in Dynamics, P.J. Holmes (ed.) SIAM, Philadelphia, PA. 3 11-322.
    • (1980) New Approaches to Nonlinear Problems in Dynamics , vol.3 , pp. 11-322
    • Ueda, Y.1
  • 106
    • 15244341733 scopus 로고
    • Amplitude instability and ergodic behavior for conservative nonlinear oscillator systems
    • Walker, G.H. and Ford, J.,1969, Amplitude instability and ergodic behavior for conservative nonlinear oscillator systems, Physical Review, 188, 416-432.
    • (1969) Physical Review , vol.188 , pp. 416-432
    • Walker, G.H.1    Ford, J.2
  • 107
    • 0008494528 scopus 로고
    • Determining Lyapunov exponents fiom a time series
    • Wolf, A., Swift, J., Swinney, S. and Vastano, J., 1985, Determining Lyapunov exponents fiom a time series, Physica D, 16,285-3 17.
    • (1985) Physica D , vol.16
    • Wolf, A.1    Swift, J.2    Swinney, S.3    Vastano, J.4
  • 108
    • 84967630003 scopus 로고    scopus 로고
    • On the computation of Lyapunov exponents for forced vibration of a Lennard-Jones Oscillator, Chaos, and flow
    • Nonlinearity, 7,44 1-473. 5, 385-401. cs JEPT, 82, 1190-1 195
    • Yang, G., Lu, J. and Luo, A.C.J., 2005, On the computation of Lyapunov exponents for forced vibration of a Lennard-Jones Oscillator, Chaos, and flow, Physica D, 43,229-268. Nonlinearity, 7,44 1-473. 5, 385-401. cs JEPT, 82, 1190-1 195.
    • (2005) Physica D , vol.43 , pp. 229-268
    • Yang, G.1    Lu, J.2    Luo, A.C.J.3
  • 109
    • 33745501553 scopus 로고    scopus 로고
    • Existence and construction of dynamical potential in nonequilibrium process without detailed balance
    • Yin, L. and Ao, P., 2006, Existence and construction of dynamical potential in nonequilibrium process without detailed balance, Journal of Physics A: Mathematical and General, 39, 8593-8601.
    • (2006) Journal of Physics A: Mathematical and General , vol.39 , pp. 8593-8601
    • Yin, L.1    Ao, P.2
  • 111
    • 0242625567 scopus 로고
    • On the mechanism of one-dimensional Fermi acceleration
    • translation: Soviet Physics-Doklady 1965, 9,989-992
    • Zaslavsky, G.M. and Chirikov, B.V., 1964, On the mechanism of one-dimensional Fermi acceleration, Doklady of Akademy Nauk 159, 306-309 (translation: Soviet Physics-Doklady 1965, 9,989-992)
    • (1964) Doklady of Akademy Nauk , vol.159 , pp. 306-309
    • Zaslavsky, G.M.1    Chirikov, B.V.2
  • 112
    • 0001585893 scopus 로고
    • Stochastic instability of trapped particles and conditions of application of the quasi-linear approximation
    • Zaslavsky, G.M. and Filonenko, N.N., 1968, Stochastic instability of trapped particles and conditions of application of the quasi-linear approximation, Soviet Physics JETP, 27, 851-857.
    • (1968) Soviet Physics JETP , vol.27 , pp. 851-857
    • Zaslavsky, G.M.1    Filonenko, N.N.2
  • 113
    • 0000652442 scopus 로고
    • Stochastic Instability of nonlinear oscillations
    • Zaslavsky, G.M. and Chirikov, B.V., 1972, Stochastic Instability of nonlinear oscillations, Soviet Physics USP, 52,263-272, 113.
    • (1972) Soviet Physics USP , vol.52
    • Zaslavsky, G.M.1    Chirikov, B.V.2
  • 114
    • 0001228181 scopus 로고
    • Scaling properties and anomalous transport of particles inside the stochastic layer
    • Zaslavsky, G.M. and Abdullaev, S.S., 1995, Scaling properties and anomalous transport of particles inside the stochastic layer, Physical Review E, 51, 3901-3910.
    • (1995) Physical Review E , vol.51 , pp. 3901-3910
    • Zaslavsky, G.M.1    Abdullaev, S.S.2


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