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

DOI10.1016/S0167-2789(01)00373-6zbMath1058.37042OpenAlexW2091965884MaRDI QIDQ5954919

David C. Diminnie, Richard Haberman

Publication date: 5 February 2002

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

Full work available at URL: https://doi.org/10.1016/s0167-2789(01)00373-6

zbMATH Keywords

one-degree-of-freedom Hamiltonian systemsstrongly nonlinear oscillations

Mathematics Subject Classification ID

Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems (37J20)

Related Items (15)

Complex periodic bursting structures in the Rayleigh-van der Pol-Duffing oscillator ⋮ Interaction of sine-Gordon kinks with defects: the two-bounce resonance ⋮ Solution asymptotics for the system of Landau–Lifshitz equations under a saddle-node dynamical bifurcation ⋮ Asymptotics of Dynamical Saddle-node Bifurcations ⋮ 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 ⋮ Control of bifurcation-delay of slow passage effect by delayed self-feedback ⋮ Complex mixed-mode vibration types triggered by the pitchfork bifurcation delay in a driven van der Pol-Duffing oscillator ⋮ ACTION AND PERIOD OF HOMOCLINIC AND PERIODIC ORBITS FOR THE UNFOLDING OF A SADDLE-CENTER BIFURCATION ⋮ Homoclinic bifurcations in reversible Hamiltonian systems ⋮ Asymptotics of the solution of a differential equation in a saddle-node bifurcation ⋮ Effect of processing delay on bifurcation delay in a network of slow-fast oscillators ⋮ Averaging method for systems with separatrix crossing ⋮ Another look at the saddle-centre bifurcation: vanishing twist. ⋮ Jumps of adiabatic invariant at the separatrix of a degenerate saddle point

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