Speaker: 杨文元教授，北京大学

Inviter: 中国科学院数学院学术报告会组委

Title: Dimensions of escaping and recurrent geodesics

Language: Chinese

Time & Venue: 2025.05.16 10:40-11:50 南楼N204（数学院交流报告会）

Abstract: In this talk, we investigate the asymptotic behavior of geodesics—such as escaping and recurrent trajectories—on Riemannian manifolds. Recurrent geodesics are characterized by their endpoints in the visual boundary, which correspond to conical limit points for the fundamental group. The Hausdorff dimension of (uniformly) conical points has been extensively studied, beginning with Patterson’s work (1976) on Fuchsian groups, followed by Sullivan (1979) for geometrically finite Kleinian groups, and later Bishop-Jones (1997) for general Kleinian groups. In this talk, we extend these classical results by computing the Hausdorff dimensions of two other key subsets of the limit set: The Myrberg limit set (a distinguished subclass of non-uniformly conical points) and the non-conical limit set. This is based an ongoing joint work with Mahan Mj (TIFR).