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EnglishWe 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.
| Titolo: | Optimal stability and instability results for a class of nearly integrable Hamiltonian systems | |
| Autori: | Berti, Massimiliano; Biasco, L.; Bolle, P. | |
| Rivista: | ||
| Data di pubblicazione: | 2002 | |
| Volume: | 13 | |
| Fascicolo: | 2 | |
| Pagina iniziale: | 77 | |
| Pagina finale: | 84 | |
| URL: | https://arxiv.org/abs/math/0203188 | |
| Appare nelle tipologie: | 1.1 Journal article |
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