Vortrag "Forcing relations for periodic orbits"

Abstract 

Periodic orbits play a leading role in the study of the dynamics of iterated transformations of a given space. This talk outlines an abstract approach to the analysis of dynamical forcing relations between periodic orbits of a fixed transformation. In other words, we present a strategy to answer the following question: "Under what conditions on a space, does the existence of some periodic orbit imply, in a general way, the existence of other orbits ?". Every periodic orbit is specified by topological properties
that will serve as a base for the comparison. The expected forcing relations define a preorder on the set of such specifications. Understanding the preorder is of main interest in this context. The above framework is illustrated at its best by the Sharkovskii Theorem on interval dynamics. In dimension two, achievements have been made towards the establishment of an analogue for surface homeomorphisms.
Keywords: dynamical systems, periodic orbits, braid types, Sharkovskii’s Theorem