Hamiltonian Reduction by Stages
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Beschreibung
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.
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.
Includes supplementary material: sn.pub/extras
Autor*in
Jerrold E. Marsden
Themen in »Hamiltonian Reduction by Stages«
DEX Hamiltonian Volume distribution group identification matrices mechanics momentum reduction symmetry symplectic time
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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)
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