Academic Report of School of Mathematical Sciences [2026] No. 076

(Series Report for High-Level University Construction No. 1335)

Title：Equilibrium states for non-uniformly hyperbolic geodesic flows

Speaker：Dong Chen, Assistant Professor (Indiana University)

Time：14:30-15:30, July 3, 2026

Location：Room 1420, Huiwen Building, Yuehai Campus, Shenzhen University

Abstract: 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 and others. This work is joint with N. Kao and K. Park.

Speaker Profile：Chen Dong received his Ph.D. from Pennsylvania State University in 2017 and subsequently taught at Ohio State University and Pennsylvania State University. He is currently an assistant professor at Indiana University Indianapolis. His research focuses on the intersection of geometry and dynamical systems, and he has published numerous papers in academic journals such as Adv. Math., Transactions of the AMS, Commun. Contemp. Math., Journal of Modern Dynamics, and Journal de l'École polytechnique - Mathématiques, Nonlinearity.

Faculty and students are welcome to attend!

Invited by: Ze Zhou

School of Mathematical Sciences

July 2, 2026