Symmetry Reduction in Symplectic and Poisson Geometry |
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| Authors: | Juan-Pablo Ortega and Judor S. Ratiu |
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| Affiliation: | (1) Centre National de la Recherche Scientifique, Département de Mathématiques de Besançon, Université de Franche-Comté. UFR des Sciences et Techniques, 16, route de Gray, France;(2) Centre Bernoulli, École Polytechnique Fédérale de Lausanne, Switzerland |
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| Abstract: | We present a quick review of several reduction techniques for symplectic and Poisson manifolds using local and global symmetries compatible with these structures. Reduction based on the standard momentum map (symplectic or Marsden–Weinstein reduction) and on generalized distributions (the optimal momentum map and optimal reduction) is emphasized. Reduction of Poisson brackets is also discussed and it is shown how it defines induced Poisson structures on cosymplectic and coisotropic submanifolds. |
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| Keywords: | Poisson geometry Hamiltonian symmetries and conservation laws Momentum maps Reduction Symplectic |
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