学术报告一：Expansivity and uniqueness of equilibrium states for multi-singular hyperbolic flows and star flows

时间：2023年7月24日（星期一）上午10：00-11:00

地点：沙河校区，学院1号楼102会议室

报告人：杨帆，Wake Forest University，助理教授

报告摘要：Multi-singular hyperbolicity was introduced by Bonatti and da Luz to capture the hyperbolicity of singular star flows. In this talk, we will consider the statistical properties of multi-singular hyperbolic sets, and singular star flows in general. We will prove that typical such systems are robustly almost expansive; furthermore, equilibrium states exist and are unique for most H\"older continuous potential functions. As a corollary, we show that C^1 open and densely, star flows have finitely many measures of maximal entropy.

报告人简介：杨帆，2015年博士毕业于美国南加州大学，先后于巴西理论数学和应用数学研究所（IMPA）、里约热内卢联邦大学、俄克拉荷马大学作博士后研究，研究方向为微分动力系统与遍历论，在Trans. Amer. Math. Soc., Ann. Inst. H. Poincaré C Anal. Non Linéaire, Israel J. Math., Ergodic Theory and Dynamical Systems等知名期刊发表论文十余篇。

学术报告二：Nonuniformly hyperbolic endomorphisms

时间：2023年7月24日（星期一）上午11:00-12:00

地点：沙河校区，学院1号楼102会议室

报告人：Radu Saghin，智利瓦尔帕莱索天主教大学，副教授

报告摘要：I will present an open class of area-preserving endomorhisms on the two-torus which are nonuniformly hyperbolic, meaning that Lebesgue almost every point has nonzero exponents, one positive and one negative. These examples are stably ergodic, and the Lyapunov exponents depend continuously on the map in the $C^1$ topology. This is joint work with M. Andersson and P. Carrasco.

报告人简介：Radu Saghin，2005年博士毕业于美国西北大学，先后于多伦多大学、巴塞罗那CRM中心、巴西圣保罗大学等院所作博士后研究，研究方向为微分动力系统与遍历论，在Mem. Amer. Math. Soc., Trans. Amer. Math. Soc., Ann. Inst. H. Poincaré C Anal. Non Linéaire, Comm. Math. Phys.等期刊发表论文20余篇。