Preprint des Projektes: SFB 701: Spektrale Strukturen und Topologische Methoden in der Mathematik - Projekt A2

Numerische Spektralanalyse unendlich-dimensionaler Transferoperatoren

06-029 Thorsten Hüls.
Homoclinic Orbits of Non-Autonomous Maps and their Approximation

We consider homoclinic orbits in non-autonomous discrete time dynamical systems of the form xn+1 = fn(xn), n ∈ Z, where it is assumed that an n independent fixed point exists. A numerical method for computing finite approximations of transversal homoclinic orbits is introduced and a detailed error analysis is presented. The non-autonomous setup requires special tools. We prove that the analytic condition of transversality of the orbit corresponds to a transversal intersection of the corresponding invariant fiber bundles. The approximation method and the validity of the error estimate is illustrated by an example.