Dynamical Zeta Functions and Dynamical Determinants for Hyperbolic Maps
The spectra of transfer operators associated to dynamical systems, when acting on suitable Banach spaces, contain key information about the ergodic properties of the systems. Focusing on expanding and hyperbolic maps, this book gives a self-contained acco
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Viviane Baladi
Dynamical Zeta Functions and Dynamical Determinants for Hyperbolic Maps A Functional Approach
Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge
A Series of Modern Surveys in Mathematics
Editorial Board L. Ambrosio, Pisa V. Baladi, Paris G.-M. Greuel, Kaiserslautern M. Gromov, Bures-sur-Yvette G. Huisken, T¨ubingen J. Jost, Leipzig J. Koll´ar, Princeton G. Laumon, Orsay U. Tillmann, Oxford J. Tits, Paris D.B. Zagier, Bonn
For further volumes: www.springer.com/series/728
Volume 68
Viviane Baladi
Dynamical Zeta Functions and Dynamical Determinants for Hyperbolic Maps A Functional Approach
Viviane Baladi IMJ-PRG CNRS and Sorbonne Universit´e Paris, France
ISSN 0071-1136 ISSN 2197-5655 (electronic) Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics ISBN 978-3-319-77660-6 ISBN 978-3-319-77661-3 (eBook) DOI 10.1007/978-3-319-77661-3 Library of Congress Control Number: 2018943138 Mathematics Subject Classification: 37C30, 37D20, 37D35 © Springer International Publishing AG, part of Springer Nature 2018 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 the registered company Springer International Publishing AG part of Springer Nature. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
On July 9, 2001, Springer invited me to contribute a monograph on dynamical systems. I immediately accepted, offering to write a book on dynamical zeta functions and dynamical determinants: Dynamical determinants are functions defined from weighted periodic orbit data of a differentiable dynamical system. The zeroes of these functions describe a large part of the spectrum of an associated transfer operator. In other words they play the role of Fredholm determinants for the (usually not compact) transfer op
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