Abstract
This paper concerns Hamiltonian and non-Hamiltonian perturbations of integrable two degree of freedom Hamiltonian systems which contain homoclinic and periodic orbits. Our main example concerns perturbations of the uncoupled system consisting of the simple pendulum and the harmonic oscillator. We show that small coupling perturbations with, possibly, the addition of positive and negative damping breaks the integrability by introducing horseshoes into the dynamics.
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Communicated by D. Ruelle
Research partially supported by ARO Contract DAAG-29-79-C-0086 and by NSF Grants ENG 78-02891 and MCS-78-06718
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Holmes, P.J., Marsden, J.E. Horseshoes in perturbations of Hamiltonian systems with two degrees of freedom. Commun.Math. Phys. 82, 523–544 (1982). https://doi.org/10.1007/BF01961239
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DOI: https://doi.org/10.1007/BF01961239