A geometric proof of separatrix crossing results.

DOI10.1016/J.NA.2003.11.002zbMath1035.37042OpenAlexW1964410257MaRDI QIDQ1428429

D. Massart

Publication date: 29 March 2004

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2003.11.002

zbMATH Keywords

perturbationadiabatic invarianceone degree of freedom Hamiltonian systemseparatrix crossing results

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Adiabatic invariants for problems in Hamiltonian and Lagrangian mechanics (70H11) Perturbation theories for problems in Hamiltonian and Lagrangian mechanics (70H09)

Related Items (1)

A NONINTEGRABILITY CRITERION FOR ADIABATIC SYSTEMS

Cites Work

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• Passage through a separatrix in a resonance problem with a slowly-varying parameter
• Accuracy loss of action invariance in adiabatic change of a one-freedom Hamiltonian
• EQUIVALENCE AND NORMAL FORMS OF GERMS OF SMOOTH MAPPINGS
• On stochastic behavior of perturbed Hamiltonian systems

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