报告人：孙文祥（北京大学）

时间：2022年05月10日14:30开始

腾讯会议ID：509 381 503

摘要：A While topological entropy is an invariant for equivalent discrete systems, we proved by construction that topological entropy degenerates for continuous systems-flows with singularity: there exists a pair of equivalent flows so that one has infinite entropy and the other has zero entropy. We characterized entropy degeneracy by measure degeneracy, while the later results to density degeneracy. We constructed a 5-dimensional compact manifold M and a family of vector fields on M which preserve Lebesgue measure and share a unique singularity p. By increasing staying time near p and accumulating density of Lebesgue measure near p we get Black-Hole Like dynamical systems, which have the following properties: (1) The singularity p attracts infinite density; (2) The event horizon is manifold M; (3) The ratio between reparameterized time and original time goes to infinity Leb-a.a.; (4) The Black-Hole Like dynamics is not observable: any invariant measure except the atomic one supported on the singularity p loses its invariance; (5) The Black-Hole Like systems and Explosion Like systems are systems with opposite process of time-change.

简介：孙文祥，北京大学数学科学学院教授、博士生导师。研究领域为微分动力系统的遍历理论，主要集中在非一致双曲系统的周期逼近和周期偏差以及带奇点流的熵退化等问题。长期讲授遍历论、微分动力系统、Pesin理论等课程，解决了四个公开数学问题，在国内外学术期刊发表学术论文近50篇，著有《遍历论》和《微分遍历论》。

邀请人：周云华

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