| 书目名称 | Geodesic Flows | | 编辑 | Gabriel P. Paternain | | 视频video | | | 丛书名称 | Progress in Mathematics | | 图书封面 |  | | 描述 | The aim of this book is to present the fundamental concepts and properties of the geodesic flow of a closed Riemannian manifold. The topics covered are close to my research interests. An important goal here is to describe properties of the geodesic flow which do not require curvature assumptions. A typical example of such a property and a central result in this work is Mane‘s formula that relates the topological entropy of the geodesic flow with the exponential growth rate of the average numbers of geodesic arcs between two points in the manifold. The material here can be reasonably covered in a one-semester course. I have in mind an audience with prior exposure to the fundamentals of Riemannian geometry and dynamical systems. I am very grateful for the assistance and criticism of several people in preparing the text. In particular, I wish to thank Leonardo Macarini and Nelson Moller who helped me with the writing of the first two chapters and the figures. Gonzalo Tomaria caught several errors and contributed with helpful suggestions. Pablo Spallanzani wrote solutions to several of the exercises. I have used his solutions to write many of the hints and answers. I also wish to thank | | 出版日期 | Book 1999 | | 关键词 | Fundamental group; Loop group; Riemannian manifold; curvature; differential geometry; dynamical systems; e | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4612-1600-1 | | isbn_softcover | 978-1-4612-7212-0 | | isbn_ebook | 978-1-4612-1600-1Series ISSN 0743-1643 Series E-ISSN 2296-505X | | issn_series | 0743-1643 | | copyright | Springer Science+Business Media New York 1999 |
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发表于 2025-3-21 16:38:14
