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

Numerische Spektralanalyse unendlich-dimensionaler Transferoperatoren

06-006 Thorsten Hüls.
A Model Function for Non-Autonomous Bifurcations of Maps

In this paper, we introduce a class of one-dimensional non-autonomous dynamical systems that allows an explicit study of its orbits as well as of the solutions of the associated variational equation. Furthermore, the solution operators also have explicit representations. In a special case, the model function can be transformed into the non-autonomous Beverton-Holt equation. We use this function for analyzing various notions of non-autonomous transcritical and pitchfork bifurcations that have been recently developed in the literature.