© 2011

Geodesic and Horocyclic Trajectories

  • 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


Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Françoise Dal’Bo
    Pages 1-43
  3. Françoise Dal’Bo
    Pages 45-78
  4. Françoise Dal’Bo
    Pages 79-95
  5. Françoise Dal’Bo
    Pages 97-107
  6. Françoise Dal’Bo
    Pages 109-125
  7. Françoise Dal’Bo
    Pages 127-142
  8. Françoise Dal’Bo
    Pages 143-161
  9. Back Matter
    Pages 163-176

About this book


During the past thirty years, strong relationships have interwoven the fields of dynamical systems, linear algebra and number theory. This rapport between different areas of mathematics has enabled the resolution of some important conjectures and has in fact given birth to new ones. This book sheds light on these relationships and their applications in an elementary setting, by showing that the study of curves on a surface can lead to orbits of a linear group or even to continued fraction expansions of real numbers.

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.

This book will appeal to those with a basic knowledge of differential geometry including graduate students and experts with a general interest in the area

Françoise Dal’Bo is a professor of mathematics at the University of Rennes. Her research studies topological and metric dynamical systems in negative curvature and their applications especially to the areas of number theory and linear actions.


Fuchsian group Poincaré half plane Schottky group Topological dynamics continued fraction diophantine approximations geodesic flow horocycle flow modular group

Authors and affiliations

  1. 1.IRMARUniversity of Rennes 1Rennes CedexFrance

Bibliographic information

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