Geodesic Flows on Manifolds of Negative Curvature

Ya. G. Sinai
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Ya. G. Sinai: Russian Academy of Science, Landau Institute of Theoretical Physics

A chapter in Algorithms, Fractals, and Dynamics, 1995, pp 201-215 from Springer

Abstract: Abstract This text is based on the lectures given in the Summer school on Dynamical Systems in Trieste, June, 1992. The main motivation was to expose one of the most beautiful and classical chapters of ergodic theory using some basic achievements in the entropy theory of dynamical systems. Another reason was more pragmatic. The interest to geodesic flows on manifolds of negative curvature grew enormously during the last years due to the development of quantum class. A lot of numerical and qualitative facts discovered have mainly by physicists suggest difficult and important problems concerning the connection of eigen-values of Laplacians on compact manifolds of negative curvature and geodesics, especially closed geodesics on such manifolds. We believe that the theory which is explained below can be useful for attacking these problems.

Keywords: Stable Manifold; Negative Curvature; Geodesic Flow; Conditional Measure; Markov Partition (search for similar items in EconPapers)
Date: 1995
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4613-0321-3_18

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DOI: 10.1007/978-1-4613-0321-3_18

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