Arnold diffusion in perturbations of analytic integrable Hamiltonian systems

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January 2001, 7(1): 61-84. doi: 10.3934/dcds.2001.7.61

Arnold diffusion in perturbations of analytic integrable Hamiltonian systems

1.	Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via, 585, 08007 Barcelona, Spain
2.	Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, Ed-C3, Jordi Girona, 1-3, 08034 Barcelona, Spain

Received June 1999 Revised October 2000 Published November 2000

Abstract
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Given an analytic integrable Hamiltonian with three or more degrees of freedom, we construct, arbitrarily close to it, an analytic perturbation with transition chains whose lengths only depend on the unperturbed Hamiltonian. Then we deduce that the perturbed system has Arnold diffusion. We provide the technical details of the tools we use.

Keywords: Hamiltonian systems, heteroclinic solutions, invariant tori, Arnold diffusion..

Mathematics Subject Classification: 37J40, 37D10, 70H0.

Citation: Ernest Fontich, Pau Martín. Arnold diffusion in perturbations of analytic integrable Hamiltonian systems. Discrete & Continuous Dynamical Systems - A, 2001, 7 (1) : 61-84. doi: 10.3934/dcds.2001.7.61

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