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arXiv · 1506.00383

Kolmogorov's Theorem for Low-Dimensional Invariant Tori of Hamiltonian Systems

Pavel Plotnikov·Ivan Kuznetsov
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Abstract

In this paper the problem of persistence of invariant tori under small perturbations of integrable Hamiltonian systems is considered. The existence of one-to-one correspondence between hyperbolic invariant tori and critical points of the function $\Psi$ of two variables defined on semi-cylinder is established. It is proved that if unperturbed Hamiltonian has a saddle point, then under arbitrary perturbations there persists at least one hyperbolic torus.

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Pavel Plotnikov, Ivan Kuznetsov. 2015-06-01. Kolmogorov's Theorem for Low-Dimensional Invariant Tori of Hamiltonian Systems. https://arxiv.org/abs/1506.00383

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