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Journal Articles SIAM Journal on Applied Dynamical Systems Year : 2023

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

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.

Dates and versions

hal-03356676 , version 1 (28-09-2021)

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Adrian P. Bustamante, Cristel Chandre. Numerical computation of critical surfaces for the breakup of invariant tori in Hamiltonian systems. SIAM Journal on Applied Dynamical Systems, 2023, 22 (1), pp.483-500. ⟨10.1137/21M1448501⟩. ⟨hal-03356676⟩
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