Speaker : Professor Yun Zhao(Suzhou University)
Title : Non-additive Measure-theoretic Pressure and Applications to Dimensions of an Ergodic Measure
Time : 2012-08-24 (Fri) 16:00 -
Place : Seminar Room 617, Institute of Mathematics (NTU Campus)
Abstract: Without any additional conditions on subadditive potentials, this talk defines subadditive measure-theoretic pressure, and shows that the subadditive measure-theoretic pressure for ergodic measures can be described in terms of measure-theoretic entropy and an constant associated with the ergodic measure. Based on the definition of topological pressure on non-compact set, we give another equivalent definition of subadditive measure-theoretic pressure, and we can obtain an inverse variational principle. This paper also studies the superadditive measure-theoretic pressure which has similar formalism as the subadditive measure-theoretic pressure. Moreover, we prove that the zero of the nonadditive measure-theoretic pressure gives the lower and upper bound estimate of dimensions of an ergodic measure.