On the dynamics of geodesic flows on rank one manifolds without focal points

2017-12-28

数学科学学院

学术报告




On the dynamics of geodesic flows on rank one manifolds without focal points



吴伟胜 博士


中国农业大学





摘   要



Manifolds without focal points are natural generalizations of those of nonpositive curvature. We discuss two results on the dynamics of geodesic flows on rank one manifolds without focal points. Firstly, the uniqueness of the measure of maximal entropy (MME) for geodesic flows on rank one manifolds of nonpositive curvature was conjectured by A. Katok in 1985 and proved by G. Knieper in 1998. We present the construction of MME via Patterson-Sullivan densities and prove its uniqueness following Knieper. Then we will explain how the results can be extended to rank one manifolds without focal points. Secondly, we show that the geodesic flow on rank one manifolds without focal points is ergodic with respect to the Liouville measure.



时 间:201813日(星期三)16:00-17:00


地 点:数学学院第四报告厅



邀请人:段华贵


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