Anosov Geodesic Flows on Surfaces

2022/11/22 by Hao-Tong Yan, Yan, Hao-Tong
Mathematics · #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2211.12429

openalex publication_date 2022/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is an exposition of the major results of P. Eberlein's paper, "When is a geodesic flow of Anosov type? I," in the special case when the manifold M is a surface. We follow Eberlein's coverage closely, adding details when helpful, and taking advantage of simplifications given by the dimension two case. The objective is to give readers a more tractable introduction to the important topic of Anosov geodesic flows, which highlights key concepts and arguments without worrying about generalizations to arbitrary dimension.

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