Arnold diffusion in perturbations of analytic integrable Hamiltonian systems | Zendy

Ernest Fontich | Zendy; Pau Martı́n | Zendy

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Arnold diffusion in perturbations of analytic integrable Hamiltonian systems

Author(s) -

Ernest Fontich,

Pau Martı́n

Publication year - 2001

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2001.7.61

Subject(s) - integrable system , hamiltonian system , perturbation (astronomy) , hamiltonian (control theory) , mathematical physics , physics , superintegrable hamiltonian system , covariant hamiltonian field theory , classical mechanics , mathematics , quantum mechanics , mathematical optimization

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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