Equilibrium states for non-uniformly hyperbolic geodesic flows
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时间： 2024-06-18
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题目：Equilibrium states for non-uniformly hyperbolic geodesic flows
报告人：陈栋 助理教授
摘要：The geodesic flow over a closed negatively curved manifold is Anosov, thus any Hölder potentials have unique equilibrium states. However, it is much less known for non-uniformly hyperbolic geodesic flows. Knieper proved the uniqueness of the measure of maximal entropy for the geodesic flow on compact rank 1 non-positively curved manifolds, and it was extended by Burns, Climenhaga, Fisher, and Thompson to the uniqueness of the equilibrium states for a large class of non-zero potentials with pressure gap. In this talk, I will discuss related results for geodesic flows without focal points, and some recent results regarding potentials with pressure gap. This work is joint with N. Kao and K. Park.
报告人简介：陈栋，2017年博士毕业于美国宾夕法尼亚州立大学，曾先后任教于美国俄亥俄州立大学及宾夕法尼亚州立大学。2024年秋季起任印第安纳大学助理教授。他主要从事几何与动力系统交叉领域的研究工作，在Adv. Math., Communications in Contemporary Mathematics, Journal of Modern Dynamics, Nonlinearity 等学术期刊上发表论文多篇。
