Connection across a Separatrix with Dissipation

DOI10.1002/sapm199491295zbMath0791.34040OpenAlexW2272936824MaRDI QIDQ4286239

F. Jay Bourland, Richard Haberman

Publication date: 27 April 1994

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/sapm199491295

zbMATH Keywords

homoclinic orbitaveragingseparatrixanalytic connection formulas across the separatrixdissipative perturbation of strongly nonlinear oscillatorsMelnikov energy ideasperturbed stable manifoldsslowly varying double-well potentials

Mathematics Subject Classification ID

Related Items (7)

Slow Passage Through the Nonhyperbolic Homoclinic Orbit of the Saddle‐Center Hamiltonian Bifurcation ⋮ Higher-order Melnikov theory for adiabatic systems ⋮ 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* ⋮ The shuddering pendulum ⋮ Slow passage through a transcritical bifurcation for Hamiltonian systems and the change in action due to a nonhyperbolic homoclinic orbit ⋮ ACTION AND PERIOD OF HOMOCLINIC AND PERIODIC ORBITS FOR THE UNFOLDING OF A SADDLE-CENTER BIFURCATION

Cites Work

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• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Sustained Resonance for a Nonlinear System with Slowly Varying Coefficients
• Separatrix Crossing: Time-Invariant Potentials with Dissipation
• Averaging Methods for the Phase Shift of Arbitrarily Perturbed Strongly Nonlinear Oscillators with an Application to Capture
• Energy Bounds for the Slow Capture by a Center in Sustained Resonance
• The Modulated Phase Shift for Strongly Nonlinear, Slowly Varying, and Weakly Damped Oscillators

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