动力系统研讨班

中科院数学与系统科学研究院

数学研究所

学术报告

动力系统研讨班

报告人：董长光（南开大学）

题  目：Limit theorems in dynamical systems

时  间：2023.06.15（星期四）14:00-15:00

地  点：数学院南楼N913

摘  要：Limit theorems, such as Central limit theorem, reflect certain chaotic behavior of a dynamical system. We will survey some known results of limit theorems for various systems including Anosov diffeomorphisms. Then we will discuss some recent results for systems having zero Lyapunov exponents. For example, we have nontrivial central limit theorem for systems with zero topological entropy; we also have non-standard limit theorems for partially hyperbolic systems. This is based on joint works with Dolgopyat-Kanigowski-Nandori.

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报告人：廖灵敏（武汉大学）

题  目：Diophantine approximation with exponential approximation speed

时  间：2023.06.15（星期四）15:15-16:15

地  点：数学院南楼N913

摘  要：Given a positive real number t>0, we calculate the Hausdorff dimension of the set of the couples (x,y) in the unit square such that |qx-p_1|<q^{-t} and |qy-p_2|<e^{-q} holds for infinitely many integer triples (q, p_1,p_2) with q>0. Such a study is a generalization of the classical simultaneous Diophantine approximation by replacing the polynomial approximation speed q^{-v} (v>0) for the second coordinate y to the exponential approximation speed e^{-q}. The upper bound of the Hausdorff dimension can be easily deduced from the existing results. For the lower bound, we need to develop the Mass Transference Principle of Wang and Wu (Math. Ann 2021) to incorporate the exponential speed. This is a joint work with Bing Li, Baowei Wang, Sanju Velani and Evgeniy Zorin.