Ergodic theory and negative curvature : CIRM Jean-Morlet Chair, Fall 2013
Author(s)
Bibliographic Information
Ergodic theory and negative curvature : CIRM Jean-Morlet Chair, Fall 2013
(Lecture notes in mathematics, 2164)
Springer, c2017
- : Springer
- : SMF
Available at 37 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
-
Library, Research Institute for Mathematical Sciences, Kyoto University数研
: SpringerL/N||LNM||2164200037706578
Note
"Société mathématique de France, SMF"--Cover
"A copublication with the Société de Mathématique de France (SMF) Sold and distributed to its members by the SMF, Institut Henri Poincaré, ..."--T.p. verso
Includes bibliographical references
Description and Table of Contents
Description
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 Teichmuller theory. Finally, some complementary lectures describe the deep connections between geodesic flows in negative curvature and Diophantine approximation.
Table of Contents
Boris Hasselblatt: Preface.- Boris Hasselblatt: Introduction to Hyperbolic Dynamics and Ergodic Theory.- Jacques Hadamard: On iteration and asymptotic solutions of differential equations (translated by Boris Hasselblatt).- Barbara Schapira: Dynamics of Geodesic and Horocyclic Flows.- Keith Burns, Howard Masur, Amie Wilkinson: Ergodicity of the Weil-Petersson Geodesic Flow.- Keith Burns, Howard Masur, Carlos Matheus and Amie Wilkinson: Ergodicity of Geodesic Flows on Incomplete Negatively Curved Manifolds.-Carlos Matheus: The Dynamics of the Weil-Petersson flow.- Jouni Parkkonen, Fre de ric Paulin: A survey of some Arithmetic Applications of Ergodic Theory in Negative Curvature.
by "Nielsen BookData"