Holmes, Philip J. and Marsden, Jerrold E. (1982) Melnikov's method and Arnold diffusion for perturbations of integrable Hamiltonian systems. Journal of Mathematical Physics, 23 (4). pp. 669-675. ISSN 0022-2488. http://resolver.caltech.edu/CaltechAUTHORS:HOLjmp82
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We start with an unperturbed system containing a homoclinic orbit and at least two families of periodic orbits associated with action angle coordinates. We use Kolmogorov–Arnold–Moser (KAM) theory to show that some of the resulting tori persist under small perturbations and use a vector of Melnikov integrals to show that, under suitable hypotheses, their stable and unstable manifolds intersect transversely. This transverse intersection is ultimately responsible for Arnold diffusion on each energy surface. The method is applied to a pendulum–oscillator system.
|Additional Information:||Copyright © 1982 American Institute of Physics Received June 17, 1981; accepted for publication 23 October 1981. Research partially supported by ARO contract DAAG-29-79-C-0086 and by NSF grants ENG 78-02891 and MCS-78-06718. We thank Alan Weinstein for several helpful discussions and Allan Kaufman for suggesting a stimulating physical example.|
|Subject Keywords:||OSCILLATORS; PENDULUMS; COUPLING; HAMILTONIANS; ORBITS; INTEGRALS; TWO–DIMENSIONAL SYSTEMS; FORCES; DISTURBANCES; COORDINATES; DYNAMICS|
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|Deposited On:||30 Aug 2006|
|Last Modified:||26 Dec 2012 09:00|
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