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＜E-Book＞
Hamiltonian Reduction by Stages / by Jerrold E. Marsden, Gerard Misiolek, Juan-Pablo Ortega, Matthew Perlmutter, Tudor S. Ratiu
(Lecture Notes in Mathematics. ISSN:16179692 ; 1913)

Edition	1st ed. 2007.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	2007
Language	English
Size	XV, 524 p : online resource
Authors	*Marsden, Jerrold E author Misiolek, Gerard author Ortega, Juan-Pablo author Perlmutter, Matthew author Ratiu, Tudor S author SpringerLink (Online service)
Subjects	LCSH:Dynamical systems LCSH:Geometry, Differential LCSH:Mathematical physics FREE:Dynamical Systems FREE:Differential Geometry FREE:Theoretical, Mathematical and Computational Physics
Notes	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 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 HTTP:URL=https://doi.org/10.1007/978-3-540-72470-4

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