Openness of momentum maps and persistence of extremal relative equilibria

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• 作者：Montaldi ; James ; Tokieda ; Tadashi
• 关键词：53D20 ; 37J15 ; Symplectic geometry ; Symmetric Hamiltonian systems ; Momentum maps ; Relative equilibria
• 刊名：Topology
• 出版年：2003
• 期刊代码：59_00409383
• 类别：mt
• 出版时间：July, 2003
• 卷：42
• 期：4
• 页码：833-844
• 文件大小：162 K

摘要

We prove that for every proper Hamiltonian action of a Lie group G in finite dimensions the momentum map is locally G-open relative to its image (i.e. images of G-invariant open sets are open). As an application we deduce that in a Hamiltonian system with continuous Hamiltonian symmetries, extremal relative equilibria persist for every perturbation of the value of the momentum map, provided the isotropy subgroup of this value is compact. We also demonstrate how this persistence result applies to an example of ellipsoidal figures of rotating fluid. We also provide an example with plane point vortices which shows how the compactness assumption is related to persistence.