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Geodesic and Horocyclic Trajectories

  • Textbook
  • © 2011

Overview

Authors:
  1. Françoise Dal’Bo

    1. IRMAR, University of Rennes 1, Rennes Cedex, France

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  • Provides a useful introduction to the topological dynamics of geodesic and horocycle flows associated with surfaces of curvature -1
  • The text is ‘punctuated’ with exercises, avoiding overwhelming proofs, which are either too detailed or too succinct
  • Illustrated with over 100 figures
  • Includes supplementary material: sn.pub/extras

Part of the book series: Universitext (UTX)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-XII
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  2. Dynamics of Fuchsian groups

    • Françoise Dal’Bo
    Pages 1-43

  3. Examples of Fuchsian groups

    • Françoise Dal’Bo
    Pages 45-78

  4. Topological dynamics of the geodesic flow

    • Françoise Dal’Bo
    Pages 79-95

  5. Schottky groups and symbolic dynamics

    • Françoise Dal’Bo
    Pages 97-107

  6. Topological dynamics of the horocycle flow

    • Françoise Dal’Bo
    Pages 109-125

  7. The Lorentzian point of view

    • Françoise Dal’Bo
    Pages 127-142

  8. Trajectories and Diophantine approximations

    • Françoise Dal’Bo
    Pages 143-161

  9. Back Matter

    Pages 163-176
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Keywords

About this book

Geodesic and Horocyclic Trajectories presents an introduction to the topological dynamics of two classical flows associated with surfaces of curvature −1, namely the geodesic and horocycle flows. Written primarily with the idea of highlighting, in a relatively elementary framework, the existence of gateways between some mathematical fields, and the advantages of using them, historical aspects of this field are not addressed and most of the references are reserved until the end of each chapter in the Comments section. Topics within the text cover geometry, and examples, of Fuchsian groups; topological dynamics of the geodesic flow; Schottky groups; the Lorentzian point of view and Trajectories and Diophantine approximations.

Authors and Affiliations

  • IRMAR, University of Rennes 1, Rennes Cedex, France

    Françoise Dal’Bo

Bibliographic Information

  • Book Title: Geodesic and Horocyclic Trajectories

  • Authors: Françoise Dal’Bo

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-0-85729-073-1

  • Publisher: Springer London

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag London Limited 2011

  • Softcover ISBN: 978-0-85729-072-4Published: 25 November 2010

  • eBook ISBN: 978-0-85729-073-1Published: 12 November 2010

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: XII, 176

  • Number of Illustrations: 110 b/w illustrations

  • Additional Information: Original French edition published by EDP Sciences, CNRS Editions, France, 2007. Jointly published with EDP Sciences

  • Topics: Dynamical Systems and Ergodic Theory, Number Theory, Differential Geometry

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