Arnold diffusion in perturbations of analytic integrable Hamiltonian systems

Ernest Fontich; Pau Martín

doi:10.3934/dcds.2001.7.61

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2001, Volume 7, Issue 1: 61-84. Doi: 10.3934/dcds.2001.7.61

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Arnold diffusion in perturbations of analytic integrable Hamiltonian systems

Ernest Fontich^1, and
Pau Martín²

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

Received: June 1999

Revised: October 2000

Published: January 2001

Abstract / Introduction Related Papers Cited by

Abstract

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.

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Mathematics Subject Classification: 37J40, 37D10, 70H08.

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