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Horseshoes in Perturbations of Hamiltonian Systems with Two Degrees of Freedom

Holmes, Philip J. and Marsden, Jerrold E. (1982) Horseshoes in Perturbations of Hamiltonian Systems with Two Degrees of Freedom. Communications in Mathematical Physics, 82 (4). pp. 523-544. ISSN 0010-3616. doi:10.1007/BF01961239.

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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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Additional Information:© Springer-Verlag 1982. Communicated by D. Ruelle. RReceived June 4, 1981. Research partially supported by ARO Contract DAAG-29-79-C-0086 and by NSF Grants ENG 78-02891 and MCS-78-06718. A number of helpful comments were kindly supplied by Allan Kaufman, David Rod, and Alan Weinstein.
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Army Research Office (ARO)DAAG-29-79-C-0086
Issue or Number:4
Record Number:CaltechAUTHORS:20100812-071719986
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19400
Deposited By: Ruth Sustaita
Deposited On:13 Aug 2010 17:06
Last Modified:08 Nov 2021 23:52

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