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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