We consider nonisochronous, nearly integrable, a priori unstable Hamiltonian systems with a (trigonometric polynomial) O(μ)-perturbation which does not preserve the unperturbed tori. We prove the existence of Arnold diffusion with diffusion time T = O((1/μ) ln(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 derived from classical perturbation theory.

Drift in phase space: a new variational mechanism with optimal diffusion time / Berti, M.; Biasco, L.; Bolle, P.. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - 82:6(2003), pp. 613-664. [10.1016/S0021-7824(03)00032-1]

Drift in phase space: a new variational mechanism with optimal diffusion time

Berti, M.;
2003-01-01

Abstract

We consider nonisochronous, nearly integrable, a priori unstable Hamiltonian systems with a (trigonometric polynomial) O(μ)-perturbation which does not preserve the unperturbed tori. We prove the existence of Arnold diffusion with diffusion time T = O((1/μ) ln(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 derived from classical perturbation theory.
2003
82
6
613
664
https://www.sciencedirect.com/science/article/pii/S0021782403000321?via%3Dihub
Berti, M.; Biasco, L.; Bolle, P.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/11413
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 55
  • ???jsp.display-item.citation.isi??? 52
social impact