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

2021/09/24 by Adrián P. Bustamante, Bustamante, Adrian P., C. Chandré +1 · 1 citation
Physics and Astronomy · Engineering · Mathematics · #Quantum chaos and dynamical systems #Control and Stability of Dynamical Systems #Geometric and Algebraic Topology

paper · doi:10.48550/arxiv.2109.12235

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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