| Geodesic Flows 1999 Edition Contributor(s): Paternain, Gabriel P. (Author) |
|
 |
ISBN: 0817641440 ISBN-13: 9780817641443 Publisher: Birkhauser OUR PRICE: $104.49 Product Type: Hardcover Published: September 1999 Annotation: Geodesic flows are one of the most remarkable classes of conservative dynamical systems because they provide a unified arena in which one can explore numerous interplays among several fields, including smooth ergodic theory, symplectic and Riemannian geometry, and algebraic topology. This self-contained presentation of geodesic flows introduces and discusses a variety of methods and tools that to date are only scattered throughout the literature. The book includes a concise introduction to the geodesic flow of a complete Riemannian manifold as well as numerous exercises and examples. |
| Additional Information |
| BISAC Categories: - Mathematics | Topology - General - Medical - Mathematics | Geometry - Differential |
| Dewey: 514.74 |
| LCCN: 99038332 |
| Series: Progress in Mathematics |
| Physical Information: 0.6" H x 6.39" W x 9.51" (0.90 lbs) 149 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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 the referee for a very careful reading of the manuscript and for a large number of comments with corrections and suggestions for improvement. |