Preprint des Projektes: SFB 701: Spektrale Strukturen und Topologische Methoden in der Mathematik - Projekt B3

Numerische Analyse äquivarianter Evolutionsgleichungen

15-030 Wolf-Jürgen Beyn, Thorsten Hüls, Andre Schenke.
Symbolic Coding for Noninvertible Systems: Uniform Approximation and Numerical Computation

It is well known that the Homoclinic Theorem, which conjugates a map near a transversal homoclinic orbit to a Bernoulli subshift, extends from invertible to specific noninvertible dynamical systems. In this paper, we provide a unifying approach, which combines such a result with a fully discrete analog of the conjugacy for finite but sufficiently long orbit segments. The underlying idea is to solve appropriate discrete boundary value problems in both cases, and to use the theory of exponential dichotomies for controlling the errors. This leads to a numerical approach which allows to compute the conjugacy to any prescribed accuracy. The method is demonstrated for several examples where invertibility of the map fails in different ways.