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2023-09-01

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/207620

A Remark on the Onset of Resonance Overlap

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https://doi.org/10.1134/S1560354723040056

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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Sistemes hamiltonians, Sistemes dinàmics diferenciables, Pertorbació (Matemàtica)

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Hamiltonian systems, Differentiable dynamical systems, Perturbation (Mathematics)

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FEJOZ, Jacques and GUÀRDIA MUNÁRRIZ, Marcel. A Remark on the Onset of Resonance Overlap. Regular and Chaotic Dynamics. 2023. Vol. 28, num. 4, pags. 578-584. ISSN 1560-3547. [consulted: 8 of June of 2026]. Available at: https://hdl.handle.net/2445/207620

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