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报告题目：Propertiesof invariant measures in dynamical systems with the shadowingproperty
报告人：李健副教授（汕头大学）
报告时间：2016年7月7日（星期四）下午4:00-5:00
报告地点：四号楼4131室

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                                                               数学学院
                                                             2016年7月6日

报告摘要：

   For dynamicalsystems with the shadowing property, we provide a method ofapproximation

ofinvariant measures by ergodic measures supported on odometers andtheir almost 1-1 extensions. For a topologically transitive systemwith the shadowing property, we show that ergodic measures supportedon odometers are dense in the space of invariant measures, and thenergodic measures are generic in the space of invariant measures. Wealso show that for every $c\geq 0$ and $\eps>0$ the collection ofergodic measures (supported on almost 1-1 extensions of odometers)with entropy between $c$ and $c + \eps$ is dense in the space ofinvariant measures with entropy at least $c$. Moreover, if inaddition the entropy function is upper semi-continuous, then forevery $c\geq 0$ ergodic measures with entropy $c$ are generic in thespace of invariant measures with entropy at least $c$. This is ajoint work with Piotr Oprocha.