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

Berti, Massimiliano, Biasco, Luca, and Bolle, Philippe. "Optimal stability and instability results for a class of nearly integrable Hamiltonian systems." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 13.2 (2002): 77-84. <http://eudml.org/doc/252323>.

@article{Berti2002,
abstract = {We consider nearly integrable, non-isochronous, 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 $T_\{d\} = O((1/ \mu) \log(1/ \mu))$ 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 $T_\{d\}$ is optimal as a consequence of a general stability result proved via classical perturbation theory.},
author = {Berti, Massimiliano, Biasco, Luca, Bolle, Philippe},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Arnold diffusion; Variational methods; Shadowing theorem; Perturbation theory; Non-linear functional analysis; variational methods; perturbation theory; nonlinear functional analysis},
language = {eng},
month = {6},
number = {2},
pages = {77-84},
publisher = {Accademia Nazionale dei Lincei},
title = {Optimal stability and instability results for a class of nearly integrable Hamiltonian systems},
url = {http://eudml.org/doc/252323},
volume = {13},
year = {2002},
}

TY - JOUR
AU - Berti, Massimiliano
AU - Biasco, Luca
AU - Bolle, Philippe
TI - Optimal stability and instability results for a class of nearly integrable Hamiltonian systems
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2002/6//
PB - Accademia Nazionale dei Lincei
VL - 13
IS - 2
SP - 77
EP - 84
AB - We consider nearly integrable, non-isochronous, 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 $T_{d} = O((1/ \mu) \log(1/ \mu))$ 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 $T_{d}$ is optimal as a consequence of a general stability result proved via classical perturbation theory.
LA - eng
KW - Arnold diffusion; Variational methods; Shadowing theorem; Perturbation theory; Non-linear functional analysis; variational methods; perturbation theory; nonlinear functional analysis
UR - http://eudml.org/doc/252323
ER -