Computer Algebra Methods for Equivariant Dynamical Systems
This book starts with an overview of the research of Gröbner bases which have many applications in various areas of mathematics since they are a general tool for the investigation of polynomial systems. The next chapter describes algorithms in invariant t
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1728
Lecture Notes in Mathematics Editors: A. Dold, Heidelberg F. Takens, Groningen B. Teissier, Paris
1728
Springer
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Karin Gatermann
Computer Algebra Methods for Equivariant Dynamical Systems
Springer
Author Karin Gatermann Konrad- Zuse- Zentrum fur Informationstechnik Berlin TakustraBe 7 14195 Berlin, Germany E-mail: [email protected]
Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Gatermann, Karin: Computer algebra methods for equivariant dynamical systems / Karin Gatermann. - Berlin; Heidelberg; New York; Barcelona; Hong Kong; London; Milan; Paris; Singapore; Tokyo: Springer, 2000 (Lecture notes in mathematics; 1728) ISBN 3-540-67161-7
Mathematics Subject Classification (2000): 13PI0, 68W30, 34C 14, 58E09 ISSN 0075-8434 ISBN 3-540-67161-7 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, 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 is a company in the BertelsmannSpringer publishing group. © Springer-Verlag Berlin Heidelberg 2000 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 Printed on acid-free paper SPIN: 10724931 41/3143/du
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for my parents
Preface
The topic of. this work is a special sort of algorithms summarized under the name of Computer Algebra. Then these algorithms are applied in the theory of equivariant dynamical systems. This is an interesting combination of research which has the ability to attack problems in a challenging way. Since it is a rather new area of research more results in this direction are expected in the future. I became involved in Computer Algebra because I was a member of the department Symbolik at the Konrad Zuse-Zentrum Berlin. On the other hand I was working together with people in the dynamical systems community. This way it was natural for me to combine both research directions. WHAT IS COMPUTER ALGEBRA? Basically, Computer Algebra means computation with algebraic structures and answering questions from algebra and algebraic geometry in an algorithmic way. Of course a lot of people are using Computer Algebra Systems for simple symbolic manipulations which is below the level of research in symbolic c
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