Equivariant normal form for nondegenerate singular orbits of integrable Hamiltonian systems |
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Authors: | Eva Miranda |
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Institution: | Departament d'Àlgebra i Geometria, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Espagne; Laboratoire Émile Picard, UMR 5580 CNRS, UFR MIG, Université Toulouse III, 31062 Toulouse Cedex, France |
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Abstract: | We consider an integrable Hamiltonian system with n degrees of freedom whose first integrals are invariant under the symplectic action of a compact Lie group G. We prove that the singular Lagrangian foliation associated to this Hamiltonian system is symplectically equivalent, in a G-equivariant way, to the linearized foliation in a neighborhood of a compact singular nondegenerate orbit. We also show that the nondegeneracy condition is not equivalent to the nonresonance condition for smooth systems. |
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