Displaying similar documents to “Nonseparated manifolds and completely unstable flows.”

Topological conjugacy of cascades generated by gradient flows on the two-dimensional sphere

Andrzej Bielecki (2000)

Annales Polonici Mathematici

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This article presents a theorem about the topological conjugacy of a gradient dynamical system with a constant time step and the cascade generated by its Euler method. It is shown that on the two-dimensional sphere S² the gradient dynamical flow is, under some natural assumptions, correctly reproduced by the Euler method for a sufficiently small time step. This means that the time-map of the induced dynamical system is globally topologically conjugate to the discrete dynamical system...

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.