Stable periodic motions in the problem on passage through a separatrix

DOI10.1063/1.166236zbMath1002.34029OpenAlexW2065564288WikidataQ73463504 ScholiaQ73463504MaRDI QIDQ4934671

Vladislav V. Sidorenko, Dmitrij V. Treshev, Anatoly I. Neishtadt

Publication date: 17 January 2000

Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.166236

zbMATH Keywords

Hamiltonian systemone degree of freedomstable periodic motionsnumeric experiments

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Symmetries, invariants of ordinary differential equations (34C14) Hamilton's equations (70H05) Nonlinear dynamics in mechanics (70K99)

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Cites Work

• Diffusion of particles in a slowly modulated wave
• Passage through a separatrix in a resonance problem with a slowly-varying parameter
• Phase change between separatrix crossings
• Slowly pulsating separatrices sweep homoclinic tangles where islands must be small: an extension of classical adiabatic theory
• Probability phenomena due to separatrix crossing
• SMALL DENOMINATORS AND PROBLEMS OF STABILITY OF MOTION IN CLASSICAL AND CELESTIAL MECHANICS