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Titlebook: Hamiltonian Reduction by Stages; Jerrold E. Marsden,Gerard Misiolek,Tudor S. Ratiu Book 2007 Springer-Verlag Berlin Heidelberg 2007 DEX.Ha

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发表于 2025-3-21 16:10:27 | 显示全部楼层 |阅读模式
书目名称Hamiltonian Reduction by Stages
编辑Jerrold E. Marsden,Gerard Misiolek,Tudor S. Ratiu
视频video
概述Includes supplementary material:
丛书名称Lecture Notes in Mathematics
图书封面Titlebook: Hamiltonian Reduction by Stages;  Jerrold E. Marsden,Gerard Misiolek,Tudor S. Ratiu Book 2007 Springer-Verlag Berlin Heidelberg 2007 DEX.Ha
描述.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..
出版日期Book 2007
关键词DEX; Hamiltonian; Volume; distribution; group; identification; matrices; mechanics; momentum; reduction; symme
版次1
doihttps://doi.org/10.1007/978-3-540-72470-4
isbn_softcover978-3-540-72469-8
isbn_ebook978-3-540-72470-4Series ISSN 0075-8434 Series E-ISSN 1617-9692
issn_series 0075-8434
copyrightSpringer-Verlag Berlin Heidelberg 2007
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发表于 2025-3-21 20:49:45 | 显示全部楼层
The Physiology of the Lower Urinary Tractction theory in the general setting of symplectic manifolds. The next chapter deals with, amongst other things, the important case of cotangent bundle reduction. Both of these cases are fundamental ingredients in the reduction by stages program.
发表于 2025-3-22 00:44:40 | 显示全部楼层
发表于 2025-3-22 04:55:26 | 显示全部楼层
https://doi.org/10.1007/978-1-4757-1451-7d not have been made had we followed exclusively the purely algebraic approach in §5.2. Having said that, we will analyze the relation between the stages theorem in this chapter and that in the previous one.
发表于 2025-3-22 09:22:18 | 显示全部楼层
发表于 2025-3-22 16:23:29 | 显示全部楼层
Berthold Huppertz,Ekkehard Schleußner In this chapter we will spell out the conditions under which optimal reduction by . renders the same result as reduction in the following two stages: we first reduce by .; the resulting space inherits symmetry properties coming from the quotient Lie group . that can be used to reduce one more time.
发表于 2025-3-22 20:26:44 | 显示全部楼层
Symplectic Reductionction theory in the general setting of symplectic manifolds. The next chapter deals with, amongst other things, the important case of cotangent bundle reduction. Both of these cases are fundamental ingredients in the reduction by stages program.
发表于 2025-3-22 23:44:22 | 显示全部楼层
Stages and Coadjoint Orbits of Central Extensionsductions. To deal with this situation, we use the theory developed in the preceding chapter. The same sort of phenomenon also occurs in Lagrangian reduction by stages, as presented in Cendra, Marsden, and Ratiu [2001a].
发表于 2025-3-23 03:18:22 | 显示全部楼层
Reduction by Stages with Topological Conditionsd not have been made had we followed exclusively the purely algebraic approach in §5.2. Having said that, we will analyze the relation between the stages theorem in this chapter and that in the previous one.
发表于 2025-3-23 06:02:36 | 显示全部楼层
Optimal Orbit Reductionhat we should study is .(.)/. = .(.)/., where . := .· ⊂ ./.ʹ.. The following pages constitute an in-depth study of this quotient and its relation with new (pre)-symplectic manifolds that can be used to reproduce the classical orbit reduction program and expressions.
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