Overview
- Accessible to graduate students
- Provides introductions leading to the forefront of several current research areas
- A broad sampling of ergodic geometry
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2164)
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Table of contents (7 chapters)
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Front Matter
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Back Matter
Keywords
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.Â
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.
Editors and Affiliations
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
DOI: https://doi.org/10.1007/978-3-319-43059-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2017
Softcover ISBN: 978-3-319-43058-4Published: 20 December 2017
eBook ISBN: 978-3-319-43059-1Published: 15 December 2017
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