Displaying similar documents to “Drift and diffusion in phase space”

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

Massimiliano Berti, Luca Biasco, Philippe Bolle (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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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 / 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 T d is optimal as a consequence of a general stability result proved via classical...

Diffusion time and splitting of separatrices for nearly integrable isochronous Hamiltonian systems

Massimiliano Berti, Philippe Bolle (2000)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We consider the problem of Arnold’s diffusion for nearly integrable isochronous Hamiltonian systems. We prove a shadowing theorem which improves the known estimates for the diffusion time. We also justify for three time scales systems that the splitting of the separatrices is correctly predicted by the Poincaré-Melnikov function.