Dynamical Systems, Graphs, and Algorithms
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George Osipenko
Dynamical Systems, Graphs, and Algorithms
1889
Lecture Notes in Mathematics Editors: J.-M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris
1889
George Osipenko
Dynamical Systems, Graphs, and Algorithms
ABC
Author Prof. George Osipenko Sevastopol National Technical University 99053 Sevastopol Ukraine e-mail: [email protected]
Library of Congress Control Number: 2006930097 Mathematics Subject Classification (2000): 37Bxx, 37Cxx, 37Dxx, 37Mxx, 37Nxx, 54H20, 58A15, 58A30, 65P20 ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 ISBN-10 3-540-35593-6 Springer Berlin Heidelberg New York ISBN-13 978-3-540-35593-9 Springer Berlin Heidelberg New York DOI 10.1007/3-540-35593-6 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. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com c Springer-Verlag Berlin Heidelberg 2007 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. Typesetting by the author and SPi using a Springer LATEX package Cover design: WMXDesign GmbH, Heidelberg Printed on acid-free paper
SPIN: 11772033
VA41/3100/SPi
543210
The book is dedicated to my three sons — Valeriy, Sergey, Egor and my wife — Valentina.
Preface
The book presents constructive methods of symbolic dynamics and their applications to the study of continuous and discrete dynamical systems. The main idea is the construction of a directed graph which represents the structure of the state space for the investigated dynamical system. The book contains a sufficient number of examples of concrete dynamical systems from illustrative ones to systems of current interest. Results of their numerical simulations with detailed comments are presented. For an understanding of the book matter, it is sufficient to be acquainted with a general course of ordinary differential equations. The new theoretical results are presented with proofs; the most attention is given to their applications. The book is designed for senior students and researches engaged in applications of the dynamical systems theory. The base of the presented book is the course of lectures given during the Youth Workshop “Computer Modeling of Dynamical Systems” (June 2004, St. Petersburg) initiated and supported by the UNESCO-ROSTE. Parts of these lectures were presented in ETH, Zurich,
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