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Geodesic Flows

  • Gabriel P. Paternain

Part of the Progress in Mathematics book series (PM, volume 180)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Gabriel P. Paternain
    Pages 1-5
  3. Gabriel P. Paternain
    Pages 7-29
  4. Gabriel P. Paternain
    Pages 31-50
  5. Gabriel P. Paternain
    Pages 109-131
  6. Back Matter
    Pages 133-153

About this book

Introduction

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.

Keywords

Fundamental group Loop group Riemannian manifold curvature differential geometry dynamical systems ergodic theory homology manifold

Authors and affiliations

  • Gabriel P. Paternain
    • 1
  1. 1.Centro de MatemáticaFacultad de CienciasMontevideoUruguay

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1600-1
  • Copyright Information Birkhäuser Boston 1999
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7212-0
  • Online ISBN 978-1-4612-1600-1
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site