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Volumn 20, Issue 4, 1999, Pages 319-359

Periodic and homoclinic motions in forced, coupled oscillators

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; HARMONIC ANALYSIS; PERTURBATION TECHNIQUES;

EID: 0033347491     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008336402517     Document Type: Article
Times cited : (33)

References (35)
  • 1
    • 0001991757 scopus 로고
    • Homoclinic orbits, subharmonics and global bifurcations in forced oscillations
    • G. Barenblatt, G. Iooss, and D. D. Joseph (eds.), Pitman, London
    • Greenspan, B. D. and Holmes, P. J., 'Homoclinic orbits, subharmonics and global bifurcations in forced oscillations', in Nonlinear Dynamics and Turbulence, G. Barenblatt, G. Iooss, and D. D. Joseph (eds.), Pitman, London, 1983, pp. 172-214.
    • (1983) Nonlinear Dynamics and Turbulence , pp. 172-214
    • Greenspan, B.D.1    Holmes, P.J.2
  • 2
    • 0003285244 scopus 로고
    • Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
    • Springer-Verlag, New York
    • Guckenheimer, J. and Holmes, P., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Applied Mathematical Sciences, Vol. 42, Springer-Verlag, New York, 1983.
    • (1983) Applied Mathematical Sciences , vol.42
    • Guckenheimer, J.1    Holmes, P.2
  • 3
    • 0001423908 scopus 로고
    • Introduction to Applied Nonlinear Dynamical Systems and Chaos
    • Springer-Verlag, New York
    • Wiggins, S., Introduction to Applied Nonlinear Dynamical Systems and Chaos, Texts in Applied Mathematics, Vol. 2, Springer-Verlag, New York, 1990.
    • (1990) Texts in Applied Mathematics , vol.2
    • Wiggins, S.1
  • 5
    • 0030416838 scopus 로고    scopus 로고
    • The Melnikov theory for subharmonics and their bifurcations in forced oscillations
    • Yagasaki, K., 'The Melnikov theory for subharmonics and their bifurcations in forced oscillations', SIAM Journal on Applied Mathematics 56, 1996, 1720-1765.
    • (1996) SIAM Journal on Applied Mathematics , vol.56 , pp. 1720-1765
    • Yagasaki, K.1
  • 6
    • 0003272505 scopus 로고
    • Global Bifurcations and Chaos - Analytical Methods
    • Springer-Verlag, New York
    • Wiggins, S., Global Bifurcations and Chaos - Analytical Methods, Applied Mathematical Sciences, Vol. 73, Springer-Verlag, New York, 1988.
    • (1988) Applied Mathematical Sciences , vol.73
    • Wiggins, S.1
  • 7
    • 0003885646 scopus 로고
    • Global Dynamics, Phase Space Transport, Orbits Homoclinic to Resonances, and Applications
    • American Mathematical Society, Providence, RI
    • Wiggins, S., Global Dynamics, Phase Space Transport, Orbits Homoclinic to Resonances, and Applications, Field Institute Monographs, Vol. 1, American Mathematical Society, Providence, RI, 1993.
    • (1993) Field Institute Monographs , vol.1
    • Wiggins, S.1
  • 8
    • 0033164121 scopus 로고    scopus 로고
    • The method of Melnikov for perturbations of multi-degree-of-freedom Hamiltonian systems
    • Yagasaki, K., 'The method of Melnikov for perturbations of multi-degree-of-freedom Hamiltonian systems', Nonlinearity 12, 1999, 799-822.
    • (1999) Nonlinearity , vol.12 , pp. 799-822
    • Yagasaki, K.1
  • 9
    • 0001648393 scopus 로고
    • Chaotic dynamics of quasi-periodically forced oscillators detected by Melnikov's method
    • Yagasaki, K., 'Chaotic dynamics of quasi-periodically forced oscillators detected by Melnikov's method', SIAM Journal on Mathematical Analysis 23, 1992, 1230-1254.
    • (1992) SIAM Journal on Mathematical Analysis , vol.23 , pp. 1230-1254
    • Yagasaki, K.1
  • 10
    • 4544324715 scopus 로고
    • Chaotic motions near homoclinic manifolds and resonant tori in quasiperiodic perturbations of planar Hamiltonian systems
    • Yagasaki, K., 'Chaotic motions near homoclinic manifolds and resonant tori in quasiperiodic perturbations of planar Hamiltonian systems', Physica D 69, 1993, 232-269.
    • (1993) Physica D , vol.69 , pp. 232-269
    • Yagasaki, K.1
  • 11
    • 0005241747 scopus 로고    scopus 로고
    • Homoclinic tangles, phase locking and chaos in a two-frequency perturbation of Duffing's equation
    • Yagasaki, K., 'Homoclinic tangles, phase locking and chaos in a two-frequency perturbation of Duffing's equation', Journal of Nonlinear Sciences 9, 1999, 131-148.
    • (1999) Journal of Nonlinear Sciences , vol.9 , pp. 131-148
    • Yagasaki, K.1
  • 12
    • 0039533869 scopus 로고
    • Singular perturbation theory for homoclinic orbits in a class of near-integrable Hamiltonian systems
    • Kovačič, G., 'Singular perturbation theory for homoclinic orbits in a class of near-integrable Hamiltonian systems', Journal of Dynamics and Differential Equations 5, 1993, 559-597.
    • (1993) Journal of Dynamics and Differential Equations , vol.5 , pp. 559-597
    • Kovačič, G.1
  • 13
    • 21844500253 scopus 로고
    • Singular perturbation theory for homoclinic orbits in a class of near-integrable dissipative systems
    • Kovačič, G., 'Singular perturbation theory for homoclinic orbits in a class of near-integrable dissipative systems', SIAM Journal on Mathematical Analysis 26, 1995, 1611-1643.
    • (1995) SIAM Journal on Mathematical Analysis , vol.26 , pp. 1611-1643
    • Kovačič, G.1
  • 14
    • 0002307231 scopus 로고
    • Orbits homoclinic to resonances, with an application to chaos in a model of the forced and damped sine-Gordon equation
    • Kovačič, G. and Wiggins, S., 'Orbits homoclinic to resonances, with an application to chaos in a model of the forced and damped sine-Gordon equation', Physica D 57, 1992, 185-225.
    • (1992) Physica D , vol.57 , pp. 185-225
    • Kovačič, G.1    Wiggins, S.2
  • 15
    • 0008495183 scopus 로고
    • Orbits homoclinic to resonances: The Hamiltonian case
    • Haller, G. and Wiggins, S., 'Orbits homoclinic to resonances: The Hamiltonian case', Physica D 66, 1993, 298-346.
    • (1993) Physica D , vol.66 , pp. 298-346
    • Haller, G.1    Wiggins, S.2
  • 16
    • 21844501994 scopus 로고
    • N-pulse homoclinic orbits in perturbations of resonant Hamiltonian systems
    • Haller, G. and Wiggins, S., 'N-pulse homoclinic orbits in perturbations of resonant Hamiltonian systems', Archive for Rational Mechanics and Analysis 130, 1995, 25-101.
    • (1995) Archive for Rational Mechanics and Analysis , vol.130 , pp. 25-101
    • Haller, G.1    Wiggins, S.2
  • 17
    • 4243593317 scopus 로고
    • Multi-pulse jumping orbits and homoclinic trees in a modal truncation of the damped-forced nonlinear Schrödinger equation
    • Haller, G. and Wiggins, S., 'Multi-pulse jumping orbits and homoclinic trees in a modal truncation of the damped-forced nonlinear Schrödinger equation', Physica D 85, 1995, 311-347.
    • (1995) Physica D , vol.85 , pp. 311-347
    • Haller, G.1    Wiggins, S.2
  • 18
    • 0000318075 scopus 로고    scopus 로고
    • Geometry and chaos near resonant equilibria of 3 DOF Hamiltonian systems
    • Haller, G. and Wiggins, S., 'Geometry and chaos near resonant equilibria of 3 DOF Hamiltonian systems', Physica D 90, 1996, 319-365.
    • (1996) Physica D , vol.90 , pp. 319-365
    • Haller, G.1    Wiggins, S.2
  • 19
    • 0009887657 scopus 로고
    • The existence of arbitrarily many distinct periodic orbits in a two degree of freedom Hamiltonian system
    • Veerman, P. and Holmes, P., 'The existence of arbitrarily many distinct periodic orbits in a two degree of freedom Hamiltonian system', Physica D 14, 1985, 177-192.
    • (1985) Physica D , vol.14 , pp. 177-192
    • Veerman, P.1    Holmes, P.2
  • 22
    • 0343110294 scopus 로고
    • Resonance bands in a two degree of freedom Hamiltonian system
    • Veerman, P. and Holmes, P., 'Resonance bands in a two degree of freedom Hamiltonian system', Physica D 20, 1986, 413-422.
    • (1986) Physica D , vol.20 , pp. 413-422
    • Veerman, P.1    Holmes, P.2
  • 23
    • 0001356311 scopus 로고
    • Persistence and smoothness of invariant manifolds for flows
    • Fenichel, N., 'Persistence and smoothness of invariant manifolds for flows', Indiana University Mathematics Journal 21, 1971, 193-226.
    • (1971) Indiana University Mathematics Journal , vol.21 , pp. 193-226
    • Fenichel, N.1
  • 25
    • 0003238449 scopus 로고
    • Normally Hyperbolic Invariant Manifolds in Dynamical Systems
    • Springer-Verlag, New York
    • Wiggins, S., Normally Hyperbolic Invariant Manifolds in Dynamical Systems, Applied Mathematical Sciences, Vol. 105, Springer-Verlag, New York, 1994.
    • (1994) Applied Mathematical Sciences , vol.105
    • Wiggins, S.1
  • 26
    • 0003278586 scopus 로고
    • Mathematical Method of Classical Mechanics
    • 2nd ed., Springer-Verlag, New York
    • Arnold, V. I., Mathematical Method of Classical Mechanics, 2nd ed., Graduate Texts in Mathematics, Vol. 60, Springer-Verlag, New York, 1989.
    • (1989) Graduate Texts in Mathematics , vol.60
    • Arnold, V.I.1
  • 28
    • 0003229603 scopus 로고
    • Averaging Methods in Nonlinear Dynamical Systems
    • Springer-Verlag, New York
    • Sanders, J. A. and Verhulst, F., Averaging Methods in Nonlinear Dynamical Systems, Applied Mathematical Sciences, Vol. 59, Springer-Verlag, New York, 1985.
    • (1985) Applied Mathematical Sciences , vol.59
    • Sanders, J.A.1    Verhulst, F.2
  • 31
    • 0019666924 scopus 로고
    • A partial differential equation with infinitely many periodic orbits: Chaotic oscillations of a forced beam
    • Holmes, P. and Marsden, J., 'A partial differential equation with infinitely many periodic orbits: Chaotic oscillations of a forced beam', Archive for Rational Mechanics and Analysis 76, 1981, 135-165.
    • (1981) Archive for Rational Mechanics and Analysis , vol.76 , pp. 135-165
    • Holmes, P.1    Marsden, J.2
  • 32
    • 0242344635 scopus 로고
    • Abundance of strange attractors
    • Mora, L. and Viana, M., 'Abundance of strange attractors', Acta Mathematica 171, 1993, 1-71.
    • (1993) Acta Mathematica , vol.171 , pp. 1-71
    • Mora, L.1    Viana, M.2
  • 35
    • 84974408747 scopus 로고
    • Persistence of homoclinic tangencies in higher dimensions
    • Romero, N., 'Persistence of homoclinic tangencies in higher dimensions', Ergodic Theory Dynamical System 15, 1995, 735-757.
    • (1995) Ergodic Theory Dynamical System , vol.15 , pp. 735-757
    • Romero, N.1


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