Universitext

Geodesic and Horocyclic Trajectories

Authors: Dal’Bo, Françoise

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  • Includes exercises rather than overwhelming proofs, which are either too detailed or too succinct
  • Illustrated with over 100 figures
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eBook $59.99
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  • ISBN 978-0-85729-073-1
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Softcover $74.99
price for USA in USD
  • ISBN 978-0-85729-072-4
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About this Textbook

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.

Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $59.99
price for USA in USD
  • ISBN 978-0-85729-073-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $74.99
price for USA in USD
  • ISBN 978-0-85729-072-4
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Geodesic and Horocyclic Trajectories
Authors
Series Title
Universitext
Copyright
2011
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London Limited
Distribution Rights
Exclusive distribution rights in France: EDP Sciences, France
eBook ISBN
978-0-85729-073-1
DOI
10.1007/978-0-85729-073-1
Softcover ISBN
978-0-85729-072-4
Series ISSN
0172-5939
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