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學術報告Working Seminar in Dynamical Systems: Research on Points without Lyapunov exponents
報??告??人:田學廷 教授 (復旦大學)
時????????間:2020年6月16日(周二) 上午 9:30-10:30
地????????點:騰訊會議號: 985 750 077
主辦單位:應用數學系
聯系人:吳偉勝
聯系方式:

摘 要:It follows from Oseledec Multiplicative Ergodic Theorem (or Kingman’s sub-additive Ergodic Theorem) that the set of ‘non-typical’ points for which the Oseledec averages of a given continuous cocycle diverge has zero measure with respect to any invariant probability measure. In strong contrast, for any H¨older continuous cocycles over hyperbolic systems, in this talk we show that either all ergodic measures have same Maximal Lyapunov exponents or the set of Lyapunov ‘non-typical’ points is a dense $G_delta$ subset and carries full topological entropy and packing topological entropy. Moreover, we give an estimate of Bowen Hausdorff entropy from below by the metric entropy of ergodic measures which are not Lyapunov minimizing, and if further the function of integrable Lyapunov exponent is lower semi-continuous with respect to invariant measures, the set of Lyapunov ‘non-typical’ points carries full Bowen Hausdorff entropy.


報告人簡介:

田學廷,復旦大學數學科學學院教授,博士生導師。主要研究領域:動力系統與遍歷論。已在《 Adv. Math. 》、《 Trans. AMS 》、《 Erg. The. & Dyn. Sys. 》、《 Math. Z. 》、《 Ann I H Poincare-Prob.Stat. 》、《 Journal of Differential Equations 》、《 Nonlinearity 》等雜志上發表20余篇學術論文。


歡迎各位老師同學參加!


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