Abstract:

Certain notions of expansiveness and shadowing are defined on topological spaces, which are generalizations of the metric notions. A Topologically Anosov (TA) homeomorphism is a homeomorphism with such topological properties. We focus on plane TA homeomorphisms.

The goal of this talk is to show some examples and non-expamples of TA homeomorphisms and to prove that an orientation preserving TA homeomorphism on the plane has a fixed point.
Finally if we have time we will try to answer, at least in some cases, the following question: Is the conjugacy class of homotheties characterized by TA homeomorphisms?