Dimension Theory of Hyperbolic Flows
The dimension theory of dynamical systems has progressively developed, especially over the last two decades, into an independent and extremely active field of research. Its main aim is to study the complexity of sets and measures that are invariant under
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Luís Barreira
Dimension Theory of Hyperbolic Flows
Springer Monographs in Mathematics
For further volumes: www.springer.com/series/3733
Luís Barreira
Dimension Theory of Hyperbolic Flows
Luís Barreira Departamento de Matemática Instituto Superior Técnico Lisboa, Portugal
ISSN 1439-7382 Springer Monographs in Mathematics ISBN 978-3-319-00547-8 ISBN 978-3-319-00548-5 (eBook) DOI 10.1007/978-3-319-00548-5 Springer Cham Heidelberg New York Dordrecht London Library of Congress Control Number: 2013942381 Mathematics Subject Classification: 37C45, 37Dxx, 37Axx © Springer International Publishing Switzerland 2013 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)
To Claudia, for everything
Preface
The objective of this book is to provide a comprehensive exposition of the main results and main techniques of dimension theory and multifractal analysis of hyperbolic flows. This includes the discussion of some recent results in the area as well as some of its open problems. The book is directed to researchers as well as graduate students specializing in dynamical systems who wish to have a sufficiently comprehensive view of the theory together with a working knowledge of its main techniques. The discussion of some open problems, perhaps somewhat biased towards my own
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