Slow passage through a transcritical bifurcation for Hamiltonian systems and the change in action due to a nonhyperbolic homoclinic orbit

DOI10.1063/1.1286915zbMath0969.37028OpenAlexW2000817226WikidataQ52015747 ScholiaQ52015747MaRDI QIDQ2726388

Richard Haberman

Publication date: 17 July 2001

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

Full work available at URL: https://doi.org/10.1063/1.1286915

Mathematics Subject Classification ID

Related Items (8)

Slow Passage Through the Nonhyperbolic Homoclinic Orbit of the Saddle‐Center Hamiltonian Bifurcation ⋮ Interaction of sine-Gordon kinks with defects: the two-bounce resonance ⋮ Jump of the adiabatic invariant at a separatrix crossing: degenerate cases ⋮ An experimental study of slow passage through Hopf and pitchfork bifurcations in a parametrically driven nonlinear oscillator ⋮ ACTION AND PERIOD OF HOMOCLINIC AND PERIODIC ORBITS FOR THE UNFOLDING OF A SADDLE-CENTER BIFURCATION ⋮ Slow passage through homoclinic orbits for the unfolding of a saddle-center bifurcation and the change in the adiabatic invariant ⋮ Averaging method for systems with separatrix crossing ⋮ Jumps of adiabatic invariant at the separatrix of a degenerate saddle point

Cites Work

• Passage through a separatrix in a resonance problem with a slowly-varying parameter
• Chaotic advection in a cubic Stokes flow
• Slow passage through a saddle-center bifurcation
• Separatrix Crossing: Time-Invariant Potentials with Dissipation
• Slowly Varying Jump and Transition Phenomena Associated with Algebraic Bifurcation Problems
• Averaging Methods for the Phase Shift of Arbitrarily Perturbed Strongly Nonlinear Oscillators with an Application to Capture
• Exchange of Stabilities in Autonomous Systems
• Exchange of Stabilities in Autonomous Systems-II. Vertical Bifurcation
• Connection across a Separatrix with Dissipation
• On the asymptotic analysis of the Painleve equations via the isomonodromy method
• Changes in the adiabatic invariant and streamline chaos in confined incompressible Stokes flow
• Slow Passage Through a Pitchfork Bifurcation

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