A Remark on the Onset of Resonance Overlap

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 reson...

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Bibliographic Details
Published in:Regular & chaotic dynamics 2023, Vol.28 (4-5), p.578-584
Main Authors: Fejoz, Jacques, Guardia, Marcel
Format: Article
Language:English
Subjects:
Celestial mechanics
Criteria
Dynamic stability
Dynamical Systems
Dynamical Systems and Ergodic Theory
Hamiltonian functions
Mathematics
Mathematics and Statistics
Orbital resonances (celestial mechanics)
Parameters
Perturbation theory
Resonance
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Summary: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.
ISSN:1560-3547
1560-3547
1468-4845
DOI:10.1134/S1560354723040056