Hamiltonian Reduction by Stages [electronic resource] / by Jerrold E. Marsden, Gerard Misiolek, Juan-Pablo Ortega, Matthew Perlmutter, Tudor S. Ratiu.
Material type: TextSeries: Lecture Notes in Mathematics ; 1913Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007Description: XV, 524 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540724704Subject(s): Mathematics | Differentiable dynamical systems | Global differential geometry | Mathematical physics | Mathematics | Dynamical Systems and Ergodic Theory | Differential Geometry | Mathematical and Computational PhysicsAdditional physical formats: Printed edition:: No titleDDC classification: 515.39 | 515.48 LOC classification: QA313Online resources: Click here to access onlineCurrent library | Home library | Call number | Materials specified | URL | Status | Date due | Barcode |
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IMSc Library | IMSc Library | Link to resource | Available | EBK1863 |
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.
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