Ergodic Theory and Negative Curvature : CIRM Jean-Morlet Chair, Fall 2013 / edited by Boris Hasselblatt.

Format:

Book

Contributor:

Hasselblatt, Boris, editor.

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 2164.

Lecture Notes in Mathematics, 0075-8434 ; 2164

Language:

English

Subjects (All):

Differentiable dynamical systems.

Global differential geometry.

Dynamical Systems and Ergodic Theory.

Differential Geometry.

Local Subjects:

Dynamical Systems and Ergodic Theory.

Differential Geometry.

Physical Description:

1 online resource (VII, 328 pages 68 illustrations, 17 illustrations in color).

Contained In:

Springer eBooks

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2017.

System Details:

text file PDF

Summary:

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.

Other Format:

Printed edition:

ISBN:

9783319430591

Access Restriction:

Restricted for use by site license.