Dynamical Systems Seminar

主講者: 趙云教授 (蘇州大學 )
講題: Non-additive Measure-theoretic Pressure and Applications to Dimensions of an Ergodic Measure
時間: 2012-08-24 (Fri.)  16:00 -
地點: 數學所 617 研討室 (台大院區)
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.
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