Measures of maximal dimension on (uniformly) hyperbolic sets

Fractal Geometry and Dynamics

03 October 14:00 - 14:50

Yakov Pesin - Pennsylvania State University

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.
Kenneth Falconer
University of St Andrews
Maarit Järvenpää
University of Oulu
Antti Kupiainen
University of Helsinki
Francois Ledrappier
University of Notre Dame
Pertti Mattila
University of Helsinki


Maarit Järvenpää


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