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
Buy this book
- About this book
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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)
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Introduction to Hyperbolic Dynamics and Ergodic Theory
Pages 1-124
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On Iteration and Asymptotic Solutions of Differential Equations by Jacques Hadamard
Pages 125-128
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Dynamics of Geodesic and Horocyclic Flows
Pages 129-155
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Ergodicity of the Weil–Petersson Geodesic Flow
Pages 157-174
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Ergodicity of Geodesic Flows on Incomplete Negatively Curved Manifolds
Pages 175-208
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Table of contents (7 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Ergodic Theory and Negative Curvature
- Book Subtitle
- CIRM Jean-Morlet Chair, Fall 2013
- Editors
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- 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
