Quasi-periodic stability of normally resonant tori

2007/08/16 by Henk Broer, Henk W. Broer, Broer, Henk W. +7
Mathematics · Physics and Astronomy · #37J40 #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Photonic Systems #Quantum Chromodynamics and Particle Interactions #Quantum chaos and dynamical systems #math.DS #msc:37J40

paper · pdf · doi:10.48550/arxiv.0708.2269

openalex publication_date 2007/08/16 · arxiv created 2008/12/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study quasi-periodic tori under a normal-internal resonance, possibly with multiple eigenvalues. Two non-degeneracy conditions play a role. The first of these generalizes invertibility of the Floquet matrix and prevents drift of the lower dimensional torus. The second condition involves a Kolmogorov-like variation of the internal frequencies and simultaneously versality of the Floquet matrix unfolding. We focus on the reversible setting, but our results carry over to the Hamiltonian and dissipative contexts.

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