Quasi-Periodic Motions in Families of Dynamical Systems Order amidst
This book is devoted to the phenomenon of quasi-periodic motion in dynamical systems. Such a motion in the phase space densely fills up an invariant torus. This phenomenon is most familiar from Hamiltonian dynamics. Hamiltonian systems are well known for
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Springer Berlin Heidelberg New York Barcelona Budapest Hong Kong London Milan Paris Santa Clara Singapore Tokyo
Hendrik W. Broer George B. Huitema Mikhail B. Sevryuk
Quasi-Periodic Motions in Families of Dynamical Systems Order amidst Chaos
Springer
Authors Hendrik W. Broer Department of Mathematics University of Groningen P.O. Box 800 NL-9700 AV Groningen, The Netherlands e-mail: [email protected]
Mikhail B. Sevryuk Institute of Energy Problems of Chemical Physics Lenin prospect 38, Bldg. 2 117829 Moscow, Russia e-mail: [email protected]
George B. Huitema KPN Research P.O. Box 15000 NL-9700 CD Groningen, The Netherlands e-mail: [email protected] Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Broer, Hendrik W.: Quasi-periodic motions in families of dynamical systems: order amidst chaos / Hendrik W. Broer; George B. Huitema ; Mikhail B. Sevryuk. - Berlin; Heidelberg; New York; Barcelona; Budapest; Hong Kong; London; Milan; Paris; Santa Clara; Singapore; Tokyo: Springer, 1996 (Lecture notes in mathematics; 1645) ISBN 3-540-62025-7 NE: Huitema, George B.:; Sevrjuk, Michail B.:; GT
Mathematics Subject Classification (1991): 58F27, 58F30, 34C50, 70H05, 34030, 34C20, 11 K60, 34020, 70K30, 34C23 ISSN 0075-8434 ISBN 3-540-62025-7 Springer-Verlag Berlin Heidelberg New York First Reprint 2002 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. re-use of illustrations, recitation, broadcasting. reproduction on microfilms 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 for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg New York a part of Springer Science+Business Media © Springer-Verlag Berlin Heidelberg 1996 Printed in Germany 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: Camera-ready TEX output by the author SPIN: 10997413 46/3111 - 5 4 3 2 - Printed on acid-free paper
Preface This book is devoted to the phenomenon of quasi-periodic motion in dynamical systems. Such a motion in the phase space densely fills up an invariant torus. This phenomenon is most familiar from Hamiltonian dynamics. Hamiltonian systems are well known for their use in modelling the dynamics related to frictionless mechanics, including the planetary and lunar motions. In this context the general picture appears to be as follows. On the one hand, Hamiltonian systems occur that are in complete order: these are the integrable systems where all motion is confine
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