Clark Butler
The Ohio State University
Title
Construction of equilibrium states for Anosov flows through leaf metrics
Abstract
We discuss a new construction of equilibrium states for Anosov flows which replaces the variational principle for pressure with a variational principle for a dimensional quantity that arises naturally in many rigidity problems. Our focus will be on the step of the construction where families of leaf metrics derived from the potential are used to realize the unstable conditional measures for an equilibrium state as Hausdorff measures on unstable leaves. We will also highlight applications to pinching rigidity theorems for Anosov diffeomorphisms on T^3 and connections to recent work of Humbert on unstable entropy and u-mmes for these diffeomorphisms.
