Geodesic
Optimal stability and instability results for a class of nearly integrable Hamiltonian systems
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 13 (2002) no. 2, pp. 77-84 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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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. 
@article{RLIN_2002_9_13_2_a1,
     author = {Berti, Massimiliano and Biasco, Luca and Bolle, Philippe},
     title = {Optimal stability and instability results for a class of nearly integrable {Hamiltonian} systems},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {77--84},
     year = {2002},
     volume = {Ser. 9, 13},
     number = {2},
     zbl = {1072.37060},
     mrnumber = {MR1949480},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_2002_9_13_2_a1/}
}
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Berti, Massimiliano; Biasco, Luca; Bolle, Philippe. Optimal stability and instability results for a class of nearly integrable Hamiltonian systems. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 13 (2002) no. 2, pp. 77-84. http://geodesic.mathdoc.fr/item/RLIN_2002_9_13_2_a1/