报告题目：Measure theoretic pressure and its applications in dimension theory
报告摘要：In this talk, we define the measure theoretic pressure. This quantity is the free energy if the measure is ergodic, and it is equal to the essential supremum of the free energy of the measures in an ergodic decomposition whenever the measure is only invariant. As an application, we find that the Hausdorff dimension of an invariant measure supported on an average conformal repeller is given by the zero of the measure theoretic pressure of this measure. Furthermore, if a hyperbolic diffeomorphism is average conformal and volume-preserving, the Hausdorff dimension of any invariant measure on the hyperbolic set is equal to the sum of the zeros of measure theoretic pressure restricted to stable and unstable directions.