Statistical Properties of Deterministic Systems

Part of Tsinghua University Texts, "Statistical Properties of Deterministic Systems" discusses the fundamental theory and computational methods of the statistical properties of deterministic discrete dynamical systems. After introducing some basic results

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TSINGHUA UNIVERSITY TEXTS Tsinghua University is one of the leading institutions in China. In Tsinghua University Texts, Tsinghua University Press and Springer will copublish texts originating from courses taught at Tsinghua University, either by lecturers of the University or lecturers from abroad. The Texts are intended for advanced undergraduate and graduate students but can also be used by researchers new to the field. Tsinghua University Texts cover basic theories, techniques and methodologies, as well as advanced topics in current research areas. They focus on mathematics, statistics, physics, chemistry, geosciences, materials science, electrical engineering, computer sciences, life sciences, architecture, social sciences, and business & management. Other areas of contemporary interest will also be included.

Jiu Ding Aihui Zhou

Statistical Properties of Deterministic Systems

With 4 figures

AUTHORS: Jiu Ding Ph.D., Professor Department of Mathematics The University of Southern Mississipi Hattiesburg, MS 39406-5045, USA Email: [email protected]

Aihui Zhou Ph.D., Professor LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190, China Email: [email protected]

__________________________________________________________ ISBN 978-7-302-18296-1 Tsinghua University Press, Beijing ISBN 978-3-540-85366-4 Springer Berlin Heidelberg New York e ISBN 978-3-540-85367-1 Springer Berlin Heidelberg New York Series ISSN 1993-0305 Tsinghua University Texts Series e ISSN 1993-0313 Tsinghua University Texts __________________________________________________________ Library of Congress Control Number: 2008932537 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the 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. Violations are liable to prosecution under the German Copyright Law. © 2009 Tsinghua University Press, Beijing and Springer-Verlag GmbH Berlin Heidelberg Co-published by Tsinghua University Press, Beijing and Springer-Verlag GmbH Berlin Heidelberg Springer is a part of Springer Science+Business Media springer.com The use of general descriptive names, registered names, trademarks, 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. Cover design: Frido Steinen-Broo, EStudio Calamar, Spain Printed on acid-free paper

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Preface Ergodic theory is a mathematical subject that studies the statistical prop