中科院数学与系统科学研究院
数学研究所
中科院华罗庚数学重点实验室
华罗庚青年数学论坛
学术报告
报告人： 魏达仁 博士（新加坡国立大学）
题 目：Sub-exponential growth in dynamical systems
时 间：2023.07.18（星期二），10:00-12:00
地 点：数学院南楼N913
摘 要：Entropy is a classical invariant in the theory of dynamical systems which measures the orbit complexity in the exponential scale. In order to measure the complexity of subexpoential systems, A. Katok and J.P. Thouvenotintroduced slow entropy in 1997. In this talk, we will discuss several results related to slow entropy, which will give the classification for several homogeneous systems and non-homogeneous systems in isomorphic class. This talk is based on several jointworks with Shilpak Banerjee, Adam Kanigowski, Philipp Kunde and Kurt Vinhage.
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华罗庚青年数学论坛学术报告
报告人： 魏达仁 博士（新加坡国立大学）
题 目：Time change rigidity for unipotent flows
时 间：2023.07.18（星期二），14:00-16:00
地 点：数学院南楼N913
摘 要：Two flows are said to be Kakutani equivalent if one is isomorphic to the other after time change, or equivalently if there are Poincare sections for the flows so that the respective induced maps are isomorphic to each other. Ratner showed that ifG=SL(2,R) and \Gamma is a lattice in G, and if U is a one parameter unipotent subgroup in G then the U action on G equipped with Haar measure is loosely Bernoulli, i.e. Kakutani equivalent to a circle rotation. Thus any two such systems SL(2,R)/\Gamma areKakutani equivalent to each other. On the other hand, Ratner showed that if G'=SL(2,R) x SL(2,R) and \Gamma' is a reducible lattice, and U' is the diagonally embedded one parameter unipotent subgroup in G', then (G'/\Gamma', U', m) is not loosely Bernoulli.We show that in fact in this case and many other situations one cannot have Kakutani equivalence between such systems unless they are actually isomorphic. This is a joint work with Elon Lindenstrauss.
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