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arXiv · 2109.12235

Numerical computation of critical surfaces for the breakup of invariant tori in Hamiltonian systems

Adrian P. Bustamante·Cristel Chandre
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Abstract

We compute the critical surface for the existence of invariant tori of a family of Hamiltonian systems with two and three degrees of freedom. We use and compare two methods to compute the critical surfaces: renormalization-group transformations and conjugation in configuration space. We unveil the presence of cusps in the critical surface for the breakup of three-dimensional invariant tori, whereas the critical surface of two-dimensional invariant tori is expected to be smooth.

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Adrian P. Bustamante, Cristel Chandre. 2021-09-24. Numerical computation of critical surfaces for the breakup of invariant tori in Hamiltonian systems. https://arxiv.org/abs/2109.12235

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