Existence of transversal homoclinic points in a degenerate case

DOI10.1216/rmjm/1181073065zbMath0724.34055OpenAlexW2044523735MaRDI QIDQ2644823

Kenneth James Palmer

Publication date: 1990

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmjm/1181073065

zbMATH Keywords

Fredholm operatorhomoclinic orbitperiodic differential equationperiodic maptransversal homoclinic pointMel'nikov functionabstract bifurcation theorem

Mathematics Subject Classification ID

Topological dynamics (37B99) Bifurcation theory for ordinary differential equations (34C23) (Semi-) Fredholm operators; index theories (47A53) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (10)

Homoclinic finger-rings in \(\mathbb{R}^N\) ⋮ Exponential dichotomies and transversal homoclinic orbits in degenerate cases ⋮ Spatially localized structures in lattice dynamical systems ⋮ Tangencies between stable and unstable manifolds ⋮ Computation of bifurcation manifolds of linearly independent homoclinic orbits ⋮ Transversal homoclinic orbits for higher dimensional difference equations ⋮ TRANSVERSE HOMOCLINIC ORBIT BIFURCATED FROM A HOMOCLINIC MANIFOLD BY THE HIGHER ORDER MELNIKOV INTEGRALS ⋮ Multiple chaos arising from single-parametric perturbation of a degenerate homoclinic orbit ⋮ Discrete dichotomies and bifurcations from critical homoclinic orbits ⋮ Heteroclinic orbits in singular systems: A unifying approach

Cites Work

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• Transversal heteroclinic points and Cherry's example of a nonintegrable Hamiltonian system
• Dichotomies in stability theory
• Exponential dichotomies and transversal homoclinic points
• The Existence of Homoclinic Orbits and the Method of Melnikov for Systems in $R^n$
• Bifurcation near degenerate families
• Differentiable dynamical systems

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