Normal forms generalizing action-angle coordinates for Hamiltonian actions of Lie groups |
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Authors: | Charles-Michel Marle |
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Institution: | 1. Mathématiques, 4, Université Pierre et Marie Curie, Place Jussieu, 75230, Paris Cedex 05, France
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Abstract: | Let (M, Ω) be a symplectic manifold on which a Lie group G acts by a Hamiltonian action. Under some restrictive assumptions, we show that there exists a symplectic diffeomorphism ψ of a G-invariant open neighbourhood U of a given G-orbit in M, onto an open subset ψ(U) of a vector bundle F *, with base space G. Explicit expressions are given for the symplectic 2-form, for the momentum map and for a Hamiltonian vector field whose Hamiltonian function is G-invariant, on the model symplectic manifold ψ(U). |
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