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.
Author(s): Jerrold E. Marsden, Gerard Misiolek, Juan-Pablo Ortega, Matthew Perlmutter, Tudor S. Ratiu (auth.)
Series: Lecture Notes in Mathematics 1913
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2007
Language: English
Pages: 524
Tags: Dynamical Systems and Ergodic Theory;Differential Geometry;Mathematical and Computational Physics
Front Matter....Pages I-XV
Front Matter....Pages 1-1
Symplectic Reduction....Pages 3-42
Cotangent Bundle Reduction....Pages 43-99
The Problem Setting....Pages 101-109
Front Matter....Pages 111-111
Commuting Reduction and Semidirect Product Theory....Pages 113-142
Regular Reduction by Stages....Pages 143-175
Group Extensions and the Stages Hypothesis....Pages 177-210
Magnetic Cotangent Bundle Reduction....Pages 211-237
Stages and Coadjoint Orbits of Central Extensions....Pages 239-250
Examples....Pages 251-283
Stages and Semidirect Products with Cocycles....Pages 285-396
Reduction by Stages via Symplectic Distributions....Pages 397-407
Reduction by Stages with Topological Conditions....Pages 409-420
Front Matter....Pages 421-422
The Optimal Momentum Map and Point Reduction....Pages 423-436
Optimal Orbit Reduction....Pages 437-459
Optimal Reduction by Stages....Pages 461-481
Back Matter....Pages 483-523
