Phase change between separatrix crossings

DOI10.1016/0167-2789(89)90086-9zbMath0687.70017OpenAlexW1971636343MaRDI QIDQ1263310

John R. Cary, Rex. T. Skodje

Publication date: 1989

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(89)90086-9

zbMATH Keywords

Hamiltonian systemsseparatrix crossingscrossing parameterzero-order adiabatic approximation

Mathematics Subject Classification ID

Phase plane analysis, limit cycles for nonlinear problems in mechanics (70K05) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (17)

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 ⋮ Analysis of the separatrix map in Hamiltonian systems ⋮ Phase change and order 2 averaging for one-frequency systems with separatrix crossing* ⋮ Oscillations near a separatrix in the Duffing equation ⋮ Probability phenomena due to separatrix crossing ⋮ Scattering of trajectories at a separatrix under autoresonance ⋮ Stable periodic motions in the problem on passage through a separatrix ⋮ Slow passage through homoclinic orbits for the unfolding of a saddle-center bifurcation and the change in the adiabatic invariant ⋮ 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 ⋮ Averaging method for systems with separatrix crossing ⋮ On mechanisms of destruction of adiabatic invariance in slow–fast Hamiltonian systems ⋮ Captures into resonance and scattering on resonance in dynamics of a charged relativistic particle in magnetic field and electrostatic wave ⋮ Jumps of adiabatic invariant at the separatrix of a degenerate saddle point ⋮ A commentary ``On the periodic solutions of a forced second-order equation by S. P. Hastings and J. B. McLeod

Cites Work

• Adiabatic invariance to all orders
• On the Detection and Dynamical Consequences of Orbits Homoclinic to Hyperbolic Periodic Orbits and Normally Hyperbolic Invariant Tori in a Class of Ordinary Differential Equations
• Capture into resonance: An extension of the use of adiabatic invariants
• Asymptotic Theory of Hamiltonian and other Systems with all Solutions Nearly Periodic
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Phase change between separatrix crossings