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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

Ernest Fontich 1, and  Pau Martín 2,

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

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