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A Remark on the Onset of Resonance Overlap

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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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Regular and Chaotic Dynamics, 2023, vol. 28, num.4, p. 578-584

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Articles publicats en revistes (Matemàtiques i Informàtica)

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A Remark on the Onset of Resonance Overlap