Zero-entropy conservative homeomorphisms of hyperbolic surfaces
Fabio Tal (USP)

In some sense, the action of area-preserving homeomorphisms with zero topological entropy are the tamest possible dynamical systems one can study in surfaces, but still this is a class with a few very interesting examples. Previous works (Franks-Handel, Le Calvez-T.) have shown that when the surface is the sphere, the known examples pretty much capture the full possible spectrum of phenomena that can be observed. In this talk we will remind those results and discuss the examples that can be observed when dealing with closed hyperbolic surfaces. Time permitting, we will present a full characterization result in this setting, including a reduction theorem (by the existence of an invariant "curve") for maps that are homotopic to Dehn twists.