ACTION AND PERIOD OF HOMOCLINIC AND PERIODIC ORBITS FOR THE UNFOLDING OF A SADDLE-CENTER BIFURCATION

DOI10.1142/S0218127403008569zbMath1057.37052OpenAlexW2071597045MaRDI QIDQ4655542

David C. Diminnie, Richard Haberman

Publication date: 8 March 2005

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127403008569

zbMATH Keywords

Hamiltonian systemsMelnikov functionadiabatic invariantsactionasymptotic expansions of integralsHomoclinic orbitsunfolding of saddle-center bifurcation

Mathematics Subject Classification ID

Related Items (1)

Slow passage through homoclinic orbits for the unfolding of a saddle-center bifurcation and the change in the adiabatic invariant

Cites Work

• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Elements of applied bifurcation theory.
• Slow passage through a saddle-center bifurcation
• Slow passage through a transcritical bifurcation for Hamiltonian systems and the change in action due to a nonhyperbolic homoclinic orbit
• Slow Passage Through the Nonhyperbolic Homoclinic Orbit Associated with a Subcritical Pitchfork Bifurcation for Hamiltonian Systems and the Change in Action
• Slowly Varying Jump and Transition Phenomena Associated with Algebraic Bifurcation Problems
• Connection across a Separatrix with Dissipation
• Probability phenomena due to separatrix crossing
• Gravity waves on water of variable depth
• Asymptotic Theory of Hamiltonian and other Systems with all Solutions Nearly Periodic
• Slow passage through homoclinic orbits for the unfolding of a saddle-center bifurcation and the change in the adiabatic invariant

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