报告题目： SRB Entropy of Markov Transformations

报告人： Professor Miaohua Jiang  ( Wake Forest University )

报告时间：2022/12/16 10:00-11:00

腾讯会议：  645 943 095

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报告摘要： In the family of piecewise differentiable expanding Markov transformations, every map preserves a unique absolutely continuous invariant measure. The measure-theoretical entropy with respect to this invariant measure depends on the map differentiably. We prove that this entropy functional does not have any nontrivial local critical points. The only critical points are where the functional reaches its global maximum. We also observe that the same statement holds true for the family of sufficiently smooth volume-preserving Anosov maps on a torus. Based on Gallavotti–Cohen Chaotic Hypothesis, these families of chaotic maps may serve as mathematical models of thermodynamic systems where the second law of thermodynamics can be rigorously proved.

邀请人：陈剑宇