Asymptotic Behavior of Dynamical and Control Systems under Perturbation and Discretization
This book provides an approach to the study of perturbation and discretization effects on the long-time behavior of dynamical and control systems. It analyzes the impact of time and space discretizations on asymptotically stable attracting sets, attractor
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Lecture Notes in Mathematics Editors: J.-M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris
1783
Springer Berlin Heidelberg New York Barcelona Hong Kong London Milan Paris Singapore Tokyo
Lars Griine
Asymptotic Behavior of Dynamical and Control Systems under Perturbation and Discretization
Springer
Author Lars Griine
J. W. Goethe University
Department of Mathematics Postfach 111932 0-60054 Frankfurt, Germany e-mail: [email protected] http://www.math.uni-frankfurt.de/rvgruene
Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnmhme
Grune,Lars: Asymptotic behavior of dynamical and control systems under perturbation and discretization I Lars Grtine. - Berlin ; Heidelberg; New York; Barcelona; Hong Kong; London; Milan; Paris; Tokyo: Springer, 2002 (Lecture notes in mathematics; 1783) ISBN 3-540-43391-0
Mathematics Subject Classification (2000): 37B25,93D30, 65P40, 93B05,93B35,49L25 ISSN 0075-8434 ISBN 3-540-43391-0 Springer-Verlag Berlin Heidelberg New York 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 for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg New York a member of BertelsmannSpringer Science + Business Media GmbH http://www.springer.de C Springer-Verlag Berlin Heidelberg 2002
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: 10874150
4113142/DU- 543210 - Printed on acid-free paper
Preface
During the years in which the research results compiled in this monograph were obtained, many people contributed directly or indirectly to these results. There is, first of all, the head of our research group “Numerics, Dynamics and Optimization”, Peter E. Kloeden. I want to thank him not only for his support and his scientific interest in this work, but also for the pleasant working atmosphere and for leaving me so much time for the realization of my own research. Many thanks also go to all the other members of the group and of the Fachbereich Mathematik of the J.W. Goethe–Universit¨ at, especially to Helga Ambach for her help with all the common problems in daily university life and to Peter Bauer for keeping my computer running. A big “grazie” goes to all the members of the Dipartimento di Matematica “Guido Castelnuo
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