On the Topological Entropy of Geodesic Flows

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Reshadat, Zahra | 2019

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 53105 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Razvan, Mohammad Reza; Nassiri, Meysam
Abstract:
Let M be a connected, compact, Riemannian manifold. Geodesic flow is a flow on the unit tangent bundle of M . This flow can be studied in dynamics prespective. for example entropy or complexity of the geodesic flow. in this thesis we will follow methods of entropy estimation or computing for geodesic flow. we will follow the method of anthony manning and Ricardo Mañe for proving such result. Maning present two results linking the topological entropy of the geodesic flow on M. we expalin how he find exponential growth rate volume of balls in universal cover as a lower bound for topologycal entropy. another theorem , Mañe represent the equlity between exponential growth rate of avrage of number of geodesic
Keywords:
Geodesic Flow ; Entropy ; Riemannian Manifold ; Topological Entropy ; Upper Semicontinuous Maps