Session 7. Difference equations and their application in the mathematical modeling

Homoclinic trajectories of discrete dynamical systems

Robert Skiba, Nicolaus Copernicus University, 
The talk is based on the joint work with Jacobo Pejsachowicz
In this talk we are going to present some new results about the existence of nontrivial homoclinic trajectories of a family of discrete, nonautonomous, asymptotically hyperbolic systems parametrized by a circle which bifurcate from the trivial branch of stationary solutions. The presented results are obtained by using the topological degree theory for \(C^1\)-Fredholm maps of index zero.
References
  1. J. Pejsachowicz, R. Skiba, Global bifurcation of homoclinic trajectories of discrete dynamical systems , Cent. Eur. J. Math., Vol. 10, No. 6, 2012, 2088--2109.
  2. J. Pejsachowicz, R. Skiba, Topology and homoclinic trajectories of discrete dynamical systems, Discrete Contin. Dyn. Syst., Ser. S, Vol. 6, No. 4, 2013, 1077-1094.
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