# (OBS This talk has been canceled) Yakov Pesin: Measures of maximal dimension on (uniformly) hyperbolic sets

**Time:
**
Tue 2017-09-19 14.00 - 14.50

**Lecturer: **
Yakov Pesin, Penn State University

**Location: **
Institut Mittag-Leffler, Auravägen 17, Djursholm

In the first part of the talk I will discuss the problem of existence of measures of maximal Hausdorff dimension on repellers and (uniformly) hyperbolic sets. In the conformal case, a measure of maximal Hausdorff dimension always exists and is an invariant Gibbs measure corresponding to a specially chosen geometric potential. In general, however, there may be no invariant measures of maximal Hausdorff dimension. I then introduce the notions of Caratheodory measure and associated Caratheodory dimension which are generated by a given Holder continuous potential. This Caratheodory measure can be used as a new tool to develop thermodynamic formalism on locally maximal uniformly hyperbolic sets. In particular, applying this approach to the geometric potential gives a Gibbs measure which is the unique invariant measure of maximal Caratheodory dimension.