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Record Nr. |
UNINA9910484477503321 |
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Autore |
Marsden Jerrold E |
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Titolo |
Hamiltonian Reduction by Stages / / by Jerrold E. Marsden, Gerard Misiolek, Juan-Pablo Ortega, Matthew Perlmutter, Tudor S. Ratiu |
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Pubbl/distr/stampa |
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Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2007 |
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ISBN |
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9786610937141 |
9781280937149 |
1280937149 |
9783540724704 |
3540724702 |
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Edizione |
[1st ed. 2007.] |
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Descrizione fisica |
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1 online resource (526 p.) |
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Collana |
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Lecture Notes in Mathematics, , 0075-8434 ; ; 1913 |
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Disciplina |
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Soggetti |
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Dynamics |
Ergodic theory |
Geometry, Differential |
Mathematical physics |
Dynamical Systems and Ergodic Theory |
Differential Geometry |
Theoretical, Mathematical and Computational Physics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references (pages [483]-508) and index. |
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Nota di contenuto |
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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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Sommario/riassunto |
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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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