Hamiltonian reduction by stages
Author(s)
Bibliographic Information
Hamiltonian reduction by stages
(Lecture notes in mathematics, 1913)
Springer, c2007
Available at / 61 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||1913200001578543
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Note
Other authors: Gerard Misiołek, Juan-Pablo Ortega, Matthew Perlmutter, Tudor S. Ratiu
Bibliography: p. [483]-508
Includes index
Description and Table of Contents
Description
This volume provides a detailed account of the theory of symplectic reduction by stages, along with numerous illustrations of the theory. It gives special emphasis to group extensions, including a detailed discussion of the Euclidean group, the oscillator group, the Bott-Virasoro group and other groups of matrices. The volume also provides ample background theory on symplectic reduction and cotangent bundle reduction.
Table of Contents
Background and the Problem Setting.- Symplectic Reduction.- Cotangent Bundle Reduction.- The Problem Setting.- Regular Symplectic Reduction by Stages.- Commuting Reduction and Semidirect Product Theory.- Regular Reduction by Stages.- Group Extensions and the Stages Hypothesis.- Magnetic Cotangent Bundle Reduction.- Stages and Coadjoint Orbits of Central Extensions.- Examples.- Stages and Semidirect Products with Cocycles.- Reduction by Stages via Symplectic Distributions.- Reduction by Stages with Topological Conditions.- Optimal Reduction and Singular Reduction by Stages, by Juan-Pablo Ortega.- The Optimal Momentum Map and Point Reduction.- Optimal Orbit Reduction.- Optimal Reduction by Stages.
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