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© 2017

Ergodic Theory and Negative Curvature

CIRM Jean-Morlet Chair, Fall 2013

  • Boris Hasselblatt
  • Accessible to graduate students

  • Provides introductions leading to the forefront of several current research areas

  • A broad sampling of ergodic geometry

Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 2164)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Barbara Schapira
    Pages 129-155
  3. Keith Burns, Howard Masur, Amie Wilkinson
    Pages 157-174
  4. Keith Burns, Howard Masur, Carlos Matheus, Amie Wilkinson
    Pages 175-208
  5. Carlos Matheus
    Pages 209-291
  6. Back Matter
    Pages 327-328

About this book

Introduction

Focussing on the mathematics related to the recent proof of ergodicity of the (Weil–Petersson) geodesic flow on a nonpositively curved space whose points are negatively curved metrics on surfaces, this book provides a broad introduction to an important current area of research. It offers original textbook-level material suitable for introductory or advanced courses as well as deep insights into the state of the art of the field, making it useful as a reference and for self-study. 

The first chapters introduce hyperbolic dynamics, ergodic theory and geodesic and horocycle flows, and include an English translation of Hadamard's original proof of the Stable-Manifold Theorem. An outline of the strategy, motivation and context behind the ergodicity proof is followed by a careful exposition of it (using the Hopf argument) and of the pertinent context of Teichmüller theory. Finally, some complementary lectures describe the deep connections between geodesic flows in negative curvature and Diophantine approximation.

Keywords

ergodicity hyperbolicity geodesic flow ergodic geometry Weil-Petersson flow

Editors and affiliations

  • Boris Hasselblatt
    • 1
  1. 1.Department of MathematicsTufts UniversityMedfordUSA

Bibliographic information

  • Book Title Ergodic Theory and Negative Curvature
  • Book Subtitle CIRM Jean-Morlet Chair, Fall 2013
  • Editors Boris Hasselblatt
  • Series Title Lecture Notes in Mathematics
  • Series Abbreviated Title Lect.Notes Mathematics
  • DOI https://doi.org/10.1007/978-3-319-43059-1
  • Copyright Information Springer International Publishing Switzerland 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-319-43058-4
  • eBook ISBN 978-3-319-43059-1
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages VII, 328
  • Number of Illustrations 51 b/w illustrations, 17 illustrations in colour
  • Topics Dynamical Systems and Ergodic Theory
    Differential Geometry
  • Buy this book on publisher's site
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