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- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 1913)
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Table of contents (15 chapters)
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Front Matter
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Background and the Problem Setting
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Front Matter
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Regular Symplectic Reduction by Stages
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Front Matter
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Optimal Reduction and Singular Reduction by Stages, by Juan-Pablo Ortega
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Front Matter
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Back Matter
About this book
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 the Euclidean group, the oscillator group, the Bott-Virasoro group and other groups of matrices. Ample background theory on symplectic reduction and cotangent bundle reduction in particular is provided. Novel features of the book are the inclusion of a systematic treatment of the cotangent bundle case, including the identification of cocycles with magnetic terms, as well as the general theory of singular reduction by stages.
Reviews
From the reviews:
"For the first time in the literature, this book presents a detailed account of the theory of reduction by stages of Hamiltonian systems with symmetries. … It is therefore a useful tool in computing reduced spaces and the authors illustrate it with many physical examples. … The necessary background in symplectic reduction and the numerous examples which are provided make this book interesting for people new to the field, as well as for specialists." (Oana M. Dragulete, Mathematical Reviews, Issue 2008 i)
Authors and Affiliations
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California Institute of Technology, Pasadena, USA
Jerrold E. Marsden
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Department of Mathematics, University of Notre Dame, Notre Dame, USA
Gerard Misiolek
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Département de Mathématiques de Besançon, Université de Franche-Comté UFR des Sciences et Techniques, F-25030, Besançon cedex, France
Juan-Pablo Ortega
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Institute of Fundamental Sciences, Massey University, Palmerston North, New Zealand
Matthew Perlmutter
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Section de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
Tudor S. Ratiu
Bibliographic Information
Book Title: Hamiltonian Reduction by Stages
Authors: Jerrold E. Marsden, Gerard Misiolek, Juan-Pablo Ortega, Matthew Perlmutter, Tudor S. Ratiu
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-540-72470-4
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2007
Softcover ISBN: 978-3-540-72469-8Published: 29 June 2007
eBook ISBN: 978-3-540-72470-4Published: 05 June 2007
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XV, 524
Topics: Dynamical Systems and Ergodic Theory, Differential Geometry, Theoretical, Mathematical and Computational Physics