Heteroclinic orbits in slow-fast Hamiltonian systems with slow manifold bifurcations

DOI10.1007/s10884-010-9171-4zbMath1213.34072OpenAlexW2168276950WikidataQ57438290 ScholiaQ57438290MaRDI QIDQ616200

Stephen Schecter, Christos Sourdis

Publication date: 7 January 2011

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10884-010-9171-4

zbMATH Keywords

blow-upHamiltonian systemstranscritical bifurcationgeometric singular perturbation theorypitchfork bifurcation

Mathematics Subject Classification ID

Related Items (21)

Geometric singular perturbation theory for systems with symmetry ⋮ Analysis of a Shil'nikov type homoclinic bifurcation ⋮ Geometric desingularization of degenerate singularities in the presence of fast rotation: A new proof of known results for slow passage through Hopf bifurcations ⋮ Bifurcations Near the Weak Type Heterodimensional Cycle ⋮ The twisting bifurcations of double homoclinic loops with resonant eigenvalues ⋮ Homoclinic flip bifurcation with a nonhyperbolic equilibrium ⋮ Interface layer of a two-component Bose–Einstein condensate ⋮ Radial and bifurcating non-radial solutions for a singular perturbation problem in the case of exchange of stabilities ⋮ Dynamics Near the Heterodimensional Cycles with Nonhyperbolic Equilibrium ⋮ Dynamics and geometric desingularization of the multiple time scale FitzHugh Nagumo Rinzel model with fold singularity ⋮ Heterodimensional cycle bifurcation with two orbit flips ⋮ GLOBAL BIFURCATIONS NEAR A DEGENERATE HETERODIMENSIONAL CYCLE ⋮ Bifurcations of Double Homoclinic Loops in Reversible Systems ⋮ Analysis of an irregular boundary layer behavior for the steady state flow of a Boussinesq fluid ⋮ Generic unfolding of a degenerate heterodimensional cycle ⋮ BIFURCATION OF ROUGH HETEROCLINIC LOOP WITH ORBIT FLIPS ⋮ On the Profile of Globally and Locally Minimizing Solutions of the Spatially Inhomogeneous Allen–Cahn and Fisher–KPP Equations ⋮ Resonance Phenomena in a Singular Perturbation Problem in the Case of Exchange of Stabilities ⋮ Periodic orbits near a bifurcating slow manifold ⋮ DEGENERATE BIFURCATIONS OF HETERODIMENSIONAL CYCLES WITH ORBIT FLIP ⋮ The ground state of a Gross-Pitaevskii energy with general potential in the Thomas-Fermi limit

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