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Journal Articles Regular and Chaotic Dynamics Year : 2023

A Remark on the Onset of Resonance Overlap

Abstract

Chirikov’s celebrated criterion of resonance overlap has been widely used in celestial mechanics and Hamiltonian dynamics to detect global instability, but is rarely rigorous. We introduce two simple Hamiltonian systems, each depending on two parameters measuring, respectively, the distance to resonance overlap and nonintegrability. Within some thin region of the parameter plane, classical perturbation theory shows the existence of global instability and symbolic dynamics, thus illustrating Chirikov’s criterion.
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hal-04352884 , version 1 (13-04-2024)

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Jacques Fejoz, Marcel Guardia. A Remark on the Onset of Resonance Overlap. Regular and Chaotic Dynamics, 2023, 28, pp.578-584. ⟨10.1134/S1560354723040056⟩. ⟨hal-04352884⟩
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