We consider a nearly integrable, non-isochronous, a-priori unstable Hamiltonian system with a (trigonometric polynomial) O(μ)-perturbation which does not preserve the unperturbed tori. We prove the existence of Arnold diffusion with diffusion time Td=O((1/μ)log(1/μ)) by a variational method which does not require the existence of ``transition chains of tori'' provided by KAM theory. We also prove that our estimate of the diffusion time Td is optimal as a consequence of a general stability result proved via classical perturbation theory.

Optimal stability and instability results for a class of nearly integrable Hamiltonian systems / Berti, Massimiliano; Biasco, L.; Bolle, P.. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI. - ISSN 1120-6330. - 13:2(2002), pp. 77-84.

Optimal stability and instability results for a class of nearly integrable Hamiltonian systems

Berti, Massimiliano;
2002

Abstract

We consider a nearly integrable, non-isochronous, a-priori unstable Hamiltonian system with a (trigonometric polynomial) O(μ)-perturbation which does not preserve the unperturbed tori. We prove the existence of Arnold diffusion with diffusion time Td=O((1/μ)log(1/μ)) by a variational method which does not require the existence of ``transition chains of tori'' provided by KAM theory. We also prove that our estimate of the diffusion time Td is optimal as a consequence of a general stability result proved via classical perturbation theory.
13
2
77
84
https://arxiv.org/abs/math/0203188
Berti, Massimiliano; Biasco, L.; Bolle, P.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/16882
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