Arnold diffusion in perturbations of analytic integrable Hamiltonian systems

Pages: 61 - 84, Volume 7, Issue 1, January 2001

doi:10.3934/dcds.2001.7.61       Abstract        Full Text (297.6K)       Related Articles

Ernest Fontich - Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via, 585, 08007 Barcelona, Spain (email)
Pau Martín - Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, Ed-C3, Jordi Girona, 1-3, 08034 Barcelona, Spain (email)

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.

Keywords:  Hamiltonian systems, invariant tori, heteroclinic solutions, Arnold diffusion.
Mathematics Subject Classification:  37J40, 37D10, 70H08.

Received: June 1999;      Revised: October 2000;      Published: November 2000.