Displaying similar documents to “Bifurcation of heteroclinic orbits for diffeomorphisms”

Global bifurcation of homoclinic trajectories of discrete dynamical systems

Jacobo Pejsachowicz, Robert Skiba (2012)

Open Mathematics

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We prove the existence of an unbounded connected branch of nontrivial homoclinic trajectories of a family of discrete nonautonomous asymptotically hyperbolic systems parametrized by a circle under assumptions involving topological properties of the asymptotic stable bundles.

On the existence of chaotic behaviour of diffeomorphisms

Michal Fečkan (1993)

Applications of Mathematics

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For several specific mappings we show their chaotic behaviour by detecting the existence of their transversal homoclinic points. Our approach has an analytical feature based on the method of Lyapunov-Schmidt.