On Some Aspects of the Theory of Anosov Systems With a Survey by Ric
In this book the seminal 1970 Moscow thesis of Grigoriy A. Margulis is published for the first time. Entitled "On Some Aspects of the Theory of Anosov Systems", it uses ergodic theoretic techniques to study the distribution of periodic orbits of Ano
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Springer-Verlag Berlin Heidelberg GmbH
Grigoriy A. Margulis
On Some Aspects of the Theory of Anosov Systems With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows
Springer
Grigoriy A. Margulis Department of Mathematics Yale University 10 Hillhouse Avenue New Haven, CT 06520-8283, USA e-mail: [email protected]
Richard Sharp Department of Mathematics University of Manchester Oxford Road Manchester M13 9PL, United Kingdom e-mail: [email protected]
Translated from the Russian by Szulikowska Valentina Vladimirovna NIC "Regular and Chaotic Dynamics'~ Izhevsk, Russia
Cataloging-in-Publication Data applied for A catalog record for this book is available from the Library of Congress. Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at .
Mathematics Subject Classification (2000): 37A05, 37AlO, 37BlO, 37ClO, 37C27, 37C30, 37C35, 37C40, 37D20, 37D35, 37D40 ISSN 1439-7382 ISBN 978-3-642-07264-2 ISBN 978-3-662-09070-1 (eBook) DOI 10.1007/978-3-662-09070-1 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specificaUythe rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Berlin Heidelberg GmbH. Violations are liable for prosecution under the German Copyright Law. springeronline.com © Springer-Verlag Berlin Heidelberg 2004 Originally published by Springer-Verlag Berlin Heidelberg New York in 2004 Softcover reprint of the hardcover 1St edition 2004 The use of general descriptive names, registered names, trademarks, etc. in this publication does not intply, 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. Typeset by the authors. Edited and reformatted by Johannes Kiister, typoma, www.typoma.com Cover design: Erich Kirchner. Heidelberg 44/3142LK - 5 4 3 2 1 0 Printed on acid-free paper
Preface
I am very thankful to Springer-Verlag for publishing a translation of my thesis, which was defended at Moscow State University in 1970. There have been only two publications related to the thesis. The first one is a short announcement [4], and the second one is [17] which more or less coincides with sections 3 and 4 of the thesis. In the early seventies, I was planning to publish the thesis in its entirety, but those plans were postponed eventually for more than 30 years. The main reason for the postponement was that I became more involved in other projects. About three years ago I wrote to Joachim Heinze with the suggestion to publish an English transla
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