Multiple homoclinic orbits in conservative and reversible systems

DOI10.1090/S0002-9947-05-03793-1zbMath1162.34034OpenAlexW2116661090MaRDI QIDQ5714404

Ale Jan Homburg, Jürgen Knobloch

Publication date: 2 January 2006

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-05-03793-1

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (17)

Normal forms for equivariant differential equations ⋮ CODIMENSION 3 HETEROCLINIC BIFURCATIONS WITH ORBIT AND INCLINATION FLIPS IN REVERSIBLE SYSTEMS ⋮ The twisting bifurcations of double homoclinic loops with resonant eigenvalues ⋮ Homoclinic flip bifurcation with a nonhyperbolic equilibrium ⋮ Homoclinic flip bifurcations accompanied by transcritical bifurcation ⋮ Nongeneric bifurcations near a nontransversal heterodimensional cycle ⋮ Existence of periodic orbits and shift-invariant curve sequences near multiple homoclinics ⋮ Horseshoes for the nearly symmetric heavy top ⋮ Heterodimensional cycle bifurcation with two orbit flips ⋮ Bifurcations of Double Homoclinic Loops in Reversible Systems ⋮ Generic unfolding of a degenerate heterodimensional cycle ⋮ Codimension 3 nontwisted double homoclinic loops bifurcations with resonant eigenvalues ⋮ Homoclinic snaking near a heteroclinic cycle in reversible systems ⋮ Codimension 2 bifurcation of twisted double homoclinic loops ⋮ Is there switching for replicator dynamics and bimatrix games? ⋮ Bifurcation from codimension one relative homoclinic cycles ⋮ Codimension 2 reversible heteroclinic bifurcations with inclination flips

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