Transfer Operators, Endomorphisms, and Measurable Partitions
The subject of this book stands at the crossroads of ergodic theory and measurable dynamics. With an emphasis on irreversible systems, the text presents a framework of multi-resolutions tailored for the study of endomorphisms, beginning with a systematic
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Sergey Bezuglyi · Palle E. T. Jorgensen
Transfer Operators, Endomorphisms, and Measurable Partitions
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
Sergey Bezuglyi • Palle E. T. Jorgensen
Transfer Operators, Endomorphisms, and Measurable Partitions
123
Sergey Bezuglyi Department of Mathematics University of Iowa Iowa City Iowa, USA
Palle E. T. Jorgensen Department of Mathematics University of Iowa Iowa City Iowa, USA
ISSN 0075-8434 ISSN 1617-9692 (electronic) Lecture Notes in Mathematics ISBN 978-3-319-92416-8 ISBN 978-3-319-92417-5 (eBook) https://doi.org/10.1007/978-3-319-92417-5 Library of Congress Control Number: 2018944127 Mathematics Subject Classification (2010): Primary: 47B65, 37B45, 28D05; Secondary: 37C30, 82C41, 28D15 © 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
While the fundamental notions, transfer operators, and Laplacians over decades have played a crucial role in diverse applications, their mutual interconnections still deserve a systematic study. We begin by presenting a suitable measure theoretic framework for such a study of transfer operators, arising as part of the wider context of positive operators in measure spaces. From a long list of applicatio
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