Hamiltonian Reduction by Stages
In this volume readers will find for the first time a detailed account of the theory of symplectic reduction by stages, along with numerous illustrations of the theory. Special emphasis is given to group extensions, including a detailed discussion of
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Jerrold E. Marsden Gerard Misiołek Juan-Pablo Ortega Matthew Perlmutter Tudor S. Ratiu
Hamiltonian Reduction by Stages
1913
Lecture Notes in Mathematics Editors: J.-M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris
1913
Jerrold E. Marsden · Gerard Misiołek Juan-Pablo Ortega · Matthew Perlmutter Tudor S. Ratiu
Hamiltonian Reduction by Stages
ABC
Authors Jerrold E. Marsden CDS 107-81
Gerard Misiołek
California Institute of Technology Pasadena, CA 91125 USA e-mail: [email protected] URL: http://www.cds.caltech.edu/ ˜ marsden/
Department of Mathematics University of Notre Dame Notre Dame, IN 46556 USA e-mail: [email protected] URL: http://www.nd.edu/ ˜ mathwww/faculty/ misiolek.shtml
Juan-Pablo Ortega
Matthew Perlmutter
Centre National de la Recherche Scientifique (CNRS) D´epartement de Math´ematiques de Besançon Universit´e de Franche-Comt´e UFR des Sciences et Techniques 16, route de Gray F-25030 Besançon cedex France e-mail: [email protected] URL: http://www-math.univ-fcomte.fr/ ˜ ortega/
Institute of Fundamental Sciences Massey University Private Bag 11-222 Palmerston North New Zealand e-mail: [email protected] URL: http://www.massey.ac.nz/ ˜ wwifs/staff/ perlmutter.shtml
Tudor S. Ratiu Section de Math´ematiques Station 8 ´ Ecole Polytechnique F´ed´erale de Lausanne CH-1015, Lausanne Switzerland e-mail: tudor.ratiu@epfl.ch URL: http://cag.epfl.ch
Library of Congress Control Number: 2007927093 Mathematics Subject Classification (2000): 37-02, 37J15, 53D20, 70H03, 70H05, 70H33 ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 ISBN 978-3-540-72469-8 Springer Berlin Heidelberg New York DOI 10.1007/978-3-540-72470-4 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 authors and SPi using a Springer LATEX macro package Cover design: design & production GmbH, Heidelberg Printed on acid-free paper
SPIN: 12062669
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543210
Preface
This book is about Symplectic Reduction by Stages for Hamiltonian systems with symmetry. Reduction by stages means, roughly speaking, that we have two symmetry groups and we want to carry out symplectic reducti
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