Hamiltonian Reduction by Stages

From the reviews: "For the first time in the literature, this book presents a detailed account of the theory of reduction by stages of Hamiltonian systems with symmetries. ... It is therefore a useful tool in computing reduced spaces and the authors illustrate it with many physical examples. ... The necessary background in symplectic reduction and the numerous examples which are provided make this book interesting for people new to the field, as well as for specialists." (Oana M. Dragulete, Mathematical Reviews, Issue 2008 i)

• 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.