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Lecture Notes in Mathematics CIRM Jean-Morlet Chair Subseries
cover

Ergodic Theory and Negative Curvature

CIRM Jean-Morlet Chair, Fall 2013

Editors: Hasselblatt, Boris (Ed.)

  • Accessible to graduate students
  • Provides introductions leading to the forefront of several current research areas
  • A broad sampling of ergodic geometry
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eBook 53,54 €
price for France (gross)
  • ISBN 978-3-319-43059-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 68,56 €
price for France (gross)
  • ISBN 978-3-319-43058-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.



Table of contents (7 chapters)

Table of contents (7 chapters)
  • Introduction to Hyperbolic Dynamics and Ergodic Theory

    Pages 1-124

    Hasselblatt, Boris

  • On Iteration and Asymptotic Solutions of Differential Equations by Jacques Hadamard

    Pages 125-128

    Hasselblatt, Boris

  • Dynamics of Geodesic and Horocyclic Flows

    Pages 129-155

    Schapira, Barbara

  • Ergodicity of the Weil–Petersson Geodesic Flow

    Pages 157-174

    Burns, Keith (et al.)

  • Ergodicity of Geodesic Flows on Incomplete Negatively Curved Manifolds

    Pages 175-208

    Burns, Keith (et al.)

Buy this book

eBook 53,54 €
price for France (gross)
  • ISBN 978-3-319-43059-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 68,56 €
price for France (gross)
  • ISBN 978-3-319-43058-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

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 Volume
2164
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-43059-1
DOI
10.1007/978-3-319-43059-1
Softcover ISBN
978-3-319-43058-4
Series ISSN
0075-8434
Edition Number
1
Number of Pages
VII, 328
Number of Illustrations
51 b/w illustrations, 17 illustrations in colour
Topics