A remark about Sil'nikov saddle-focus homoclinic orbits

DOI10.3934/cpaa.2011.10.817zbMath1238.34089OpenAlexW2322268209MaRDI QIDQ652003

Flaviano Battelli, Kenneth James Palmer

Publication date: 19 December 2011

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/cpaa.2011.10.817

zbMATH Keywords

invariant manifoldstransversalityexponential dichotomyShil'nikov chaos

Mathematics Subject Classification ID

Complex behavior and chaotic systems of ordinary differential equations (34C28) Invariant manifolds for ordinary differential equations (34C45) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Dichotomy, trichotomy of solutions to ordinary differential equations (34D09) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)

Related Items (6)

Homoclinic flip bifurcation with a nonhyperbolic equilibrium ⋮ An example of Silnikov focus-focus homoclinic orbits ⋮ Dynamics Near the Heterodimensional Cycles with Nonhyperbolic Equilibrium ⋮ GLOBAL BIFURCATIONS NEAR A DEGENERATE HETERODIMENSIONAL CYCLE ⋮ Bifurcations of Double Homoclinic Loops in Reversible Systems ⋮ Shilnikov saddle-focus homoclinic orbits from numerics: higher dimensions

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