Phase change between separatrix crossings in slow–fast Hamiltonian systems

DOI10.1088/0951-7715/18/3/023zbMath1080.37064OpenAlexW2037403515MaRDI QIDQ3025251

Anatoly I. Neishtadt, Aleksey A. Vasiliev

Publication date: 13 July 2005

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0951-7715/18/3/023

zbMATH Keywords

separatrixslow-fast Hamiltonian systempseudo-phase

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Perturbations, asymptotics of solutions to ordinary differential equations (34E10)

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Stability islands in domains of separatrix crossings in slow-fast Hamiltonian systems ⋮ Asymptotic behaviour of measure for captured trajectories into parametric autoresonance ⋮ The capture of a particle into resonance at potential hole with dissipative perturbation ⋮ Phase change and order 2 averaging for one-frequency systems with separatrix crossing* ⋮ On phase at a resonance in slow-fast Hamiltonian systems ⋮ Separatrix maps in slow-fast Hamiltonian systems ⋮ Oscillations near a separatrix in the Duffing equation ⋮ Capture and holding of resonance far from equilibrium ⋮ Mixing properties of steady flow in thermocapillary driven droplets ⋮ Periodic orbits near a bifurcating slow manifold ⋮ Change of the ray propagation mode in smoothly irregular waveguides ⋮ On the absence of stable periodic orbits in domains of separatrix crossings in nonsymmetric slow-fast Hamiltonian systems ⋮ On mechanisms of destruction of adiabatic invariance in slow–fast Hamiltonian systems ⋮ Jumps of adiabatic invariant at the separatrix of a degenerate saddle point

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