Hamilton-Jacobi equation, heteroclinic chains and Arnol'd diffusion in three time scales systems

Giovanni Gallavotti; Guido Gentile; Vieri Mastropietro

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arXiv · chao-dyn/9801004

Hamilton-Jacobi equation, heteroclinic chains and Arnol'd diffusion in three time scales systems

Giovanni Gallavotti·Guido Gentile·Vieri Mastropietro

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Abstract

Interacting systems consisting of two rotators and a point mass near a hyperbolic fixed point are considered, in a case in which the uncoupled systems have three very different characteristic time scales. The abundance of quasi periodic motions in phase space is studied via the Hamilton-Jacobi equation. The main result, a high density theorem of invariant tori, is derived by the classical canonical transformation method extending previous results. As an application the existence of long heteroclinic chains (and of Arnol'd diffusion) is proved for systems interacting through a trigonometric polynomial in the angle variables.

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Giovanni Gallavotti, Guido Gentile, Vieri Mastropietro. 1998-01-02. Hamilton-Jacobi equation, heteroclinic chains and Arnol'd diffusion in three time scales systems. https://arxiv.org/abs/chao-dyn/9801004

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