Open Conformal Systems and Perturbations of Transfer Operators
The focus of this book is on open conformal dynamical systems corresponding to the escape of a point through an open Euclidean ball. The ultimate goal is to understand the asymptotic behavior of the escape rate as the radius of the ball tends to zero.&nbs
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Mark Pollicott Mariusz Urbański
Open Conformal Systems and Perturbations of Transfer Operators
Lecture Notes in Mathematics Editors-in-Chief: Jean-Michel Morel, Cachan Bernard Teissier, Paris Advisory Board: Michel Brion, Grenoble Camillo De Lellis, Zurich Alessio Figalli, Zurich Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gábor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, New York Anna Wienhard, Heidelberg
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More information about this series at http://www.springer.com/series/304
Mark Pollicott • Mariusz Urba´nski
Open Conformal Systems and Perturbations of Transfer Operators
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Mark Pollicott Department of Mathematics University of Warwick Coventry, UK
Mariusz Urba´nski Department of Mathematics University of North Texas Denton, Texas USA
ISSN 0075-8434 ISSN 1617-9692 (electronic) Lecture Notes in Mathematics ISBN 978-3-319-72178-1 ISBN 978-3-319-72179-8 (eBook) https://doi.org/10.1007/978-3-319-72179-8 Library of Congress Control Number: 2017962062 Mathematics Subject Classification (2010): 37C30, 37C45, 37C70, 37D20, 27D35, 37E05, 37F10, 37F35 © Springer International Publishing AG 2017 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. 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
We dedicate this book to the memory of Rufus Bowen on the 70th anniversary of his birth. We would like to thank Mark F. Demers for valuable comments and questions that improved the final version of our manuscript.
Preface
The escape rates thru a ball in a dynamical system have been much studied. Understanding the asymptotic behavior of the escape rate as the radius of the ball tends to zero is an especially subtle problem. In the case of hyperbolic conformal
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