Topology and homoclinic trajectories of discrete dynamicalsystems

Jacobo Pejsachowicz; Robert Skiba

doi:10.3934/dcdss.2013.6.1077

Article Contents

2013, Volume 6, Issue 4: 1077-1094. Doi: 10.3934/dcdss.2013.6.1077

This issue Previous Article Periodic solutions of second order Lagrangian difference systems with bounded or singular $\phi$-Laplacian and periodic potential Next Article Effect of positive feedback on Devil's staircase input-output relationship

Topology and homoclinic trajectories of discrete dynamical systems

Jacobo Pejsachowicz^1,2,3, and
Robert Skiba^4,5,6,

1.
Dipartamento di Matematica
2.
Politecnico di Torino
3.
Corso Duca Degli Abruzzi 24, 10129 Torino
4.
Faculty of Mathematics and Computer Science
5.
Nicolaus Copernicus University
6.
Chopina 12/18, 87-100 Toru?

Received: August 2011

Revised: October 2011

Published: August 2013

Abstract / Introduction Related Papers Cited by

Abstract

We show that nontrivial homoclinic trajectories ofa family of discrete, nonautonomous, asymptotically hyperbolic systems parametrized by a circlebifurcate from a stationary solution if the asymptotic stable bundles $E^s(+\infty)$ and$E^s(-\infty)$ of the linearization at the stationary branch are twisted in different ways.

Keywords:

Mathematics Subject Classification: 39A12, 37C29, 39A28, 47A53.

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