Shadowing and Hyperbolicity
Focusing on the theory of shadowing of approximate trajectories (pseudotrajectories) of dynamical systems, this book surveys recent progress in establishing relations between shadowing and such basic notions from the classical theory of structural stabili
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Sergei Yu. Pilyugin Kazuhiro Sakai
Shadowing and Hyperbolicity
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
Sergei Yu. Pilyugin • Kazuhiro Sakai
Shadowing and Hyperbolicity
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Sergei Yu. Pilyugin Faculty of Mathematics and Mechanics St. Petersburg State University St. Petersburg, Russia
ISSN 0075-8434 Lecture Notes in Mathematics ISBN 978-3-319-65183-5 DOI 10.1007/978-3-319-65184-2
Kazuhiro Sakai Faculty of Education Utsunomiya University Utsunomiya, Japan
ISSN 1617-9692 (electronic) ISBN 978-3-319-65184-2 (eBook)
Library of Congress Control Number: 2017950671 Mathematics Subject Classification (2010): 37C50, 37D20, 37C20, 37D30 © 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
To the memory of Dmitrii Viktorovich Anosov
Preface
The theory of shadowing of approximate trajectories (pseudotrajectories) in dynamical systems is now an important and rapidly developing branch of the modern global theory of dynamical systems. The notion of a pseudotrajectory goes back to Birkhoff [9]. The real development of the shadowing theory started after the classical results of Anosov [4] and Bowen [12]. The main results obtained in the 20th century were reflected in the monographs [64] and [56]; one can find a survey of recen
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