1.

Record Nr.

UNINA9910484477503321

Autore

Marsden Jerrold E

Titolo

Hamiltonian Reduction by Stages / / by Jerrold E. Marsden, Gerard Misiolek, Juan-Pablo Ortega, Matthew Perlmutter, Tudor S. Ratiu

Pubbl/distr/stampa

Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2007

ISBN

9786610937141

9781280937149

1280937149

9783540724704

3540724702

Edizione

[1st ed. 2007.]

Descrizione fisica

1 online resource (526 p.)

Collana

Lecture Notes in Mathematics, , 0075-8434 ; ; 1913

Disciplina

514/.74

Soggetti

Dynamics

Ergodic theory

Geometry, Differential

Mathematical physics

Dynamical Systems and Ergodic Theory

Differential Geometry

Theoretical, Mathematical and Computational Physics

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references (pages [483]-508) and index.

Nota di contenuto

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.



Sommario/riassunto

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.