Analytic and Probabilistic Approaches to Dynamics in Negative Curvature
The work of E. Hopf and G.A. Hedlund, in the 1930s, on transitivity and ergodicity of the geodesic flow for hyperbolic surfaces, marked the beginning of the investigation of the statistical properties and stochastic behavior of the flow. The first central
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Françoise Dal'Bo Marc Peigné Andrea Sambusetti Editors
Analytic and Probabilistic Approaches to Dynamics in Negative Curvature
Springer INdAM Series Volume 9
Editor-in-Chief V. Ancona Series Editors P. Cannarsa C. Canuto G. Coletti P. Marcellini G. Patrizio T. Ruggeri E. Strickland A. Verra
For further volumes: http://www.springer.com/series/10283
Françoise Dal’Bo • Marc Peigné • Andrea Sambusetti Editors
Analytic and Probabilistic Approaches to Dynamics in Negative Curvature
123
Editors Françoise Dal’Bo IRMAR Université de Rennes 1 Rennes France
Marc Peigné Lab. de Mathématiques et Physique Université François Rabelais Tours France
Andrea Sambusetti Dipartimento di Matematica Sapienza - UniversitJa di Roma Roma Italy
ISSN 2281-518X ISSN 2281-5198 (electronic) Springer INdAM Series ISBN 978-3-319-04806-2 ISBN 978-3-319-04807-9 (eBook) DOI 10.1007/978-3-319-04807-9 Springer Cham Heidelberg New York Dordrecht London Library of Congress Control Number: 2014943952 © Springer International Publishing Switzerland 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
The ergodicity of the geodesic flow .gt /t 2R with respect to the Liouville measure m on the unit tangent bundle T 1 S of a compact surface (or of finite area) with curvature 1 was ori
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