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

Massimiliano Berti; Philippe Bolle

Displaying similar documents to “Diffusion time and splitting of separatrices for nearly integrable isochronous Hamiltonian systems”

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...

Drift and diffusion in phase space

L. Chierchia, G. Gallavotti (1994)

Annales de l'I.H.P. Physique théorique

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A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: announcement of results.

Delshams, Amadeu, de la Llave, Rafael, Seara, Tere M. (2003)

Electronic Research Announcements of the American Mathematical Society [electronic only]

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A functional analysis approach to Arnold diffusion

Massimiliano Berti, Philippe Bolle (2002)

Annales de l'I.H.P. Analyse non linéaire

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Saddle-shaped solutions of bistable diffusion equations in all of ℝ2m

Xavier Cabré, Joana Terra (2009)

Journal of the European Mathematical Society

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Variational construction of homoclinics and chaos in presence of a saddle-saddle equilibrium

Massimiliano Berti, Philippe Bolle (1998)

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

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We consider autonomous Lagrangian systems possessing two homoclinic orbits to an hyperbolic equilibrium of saddle-saddle type with two different characteristic exponents. Under a nondegeneracy assumption on the homoclinics and under suitable conditions on the geometric behaviour of these homoclinics near the equilibrium we show, by variational methods, that they give rise to an infinite family of multibump homoclinic solutions. We relax the nondegeneracy assumption when the two characteristic...