TY  - BOOK
AU  - 
AU  - 
AU  - 
AU  - 
AU  - 
ED  - SpringerLink (Online service)
TI  - Hamiltonian Reduction by Stages
T2  - Lecture Notes in Mathematics,
SN  - 9783540724704
AV  - QA313 
U1  - 515.39 23
PY  - 2007///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Differentiable dynamical systems
KW  - Global differential geometry
KW  - Mathematical physics
KW  - Dynamical Systems and Ergodic Theory
KW  - Differential Geometry
KW  - Mathematical and Computational Physics
N1  - 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; ZDB-2-SMA; ZDB-2-LNM
N2  - 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
UR  - http://dx.doi.org/10.1007/978-3-540-72470-4
ER  -