Hamiltonian Reduction by Stages

Häftad, Engelska, 2007

Del 1913 i serien Lecture Notes in Mathematics

533 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2007-06-29
Mått:155 x 235 x 30 mm
Vikt:814 g
Format:Häftad
Språk:Engelska
Serie:Lecture Notes in Mathematics
Antal sidor:524
Upplaga:2007
Förlag:Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN:9783540724698

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Recensioner i media

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)

Innehållsförteckning

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.