Equivariant normal form for nondegenerate singular orbits of integrable Hamiltonian systems

Details Equivariant normal form for nondegenerate singular orbits of integrable Hamiltonian systems Equivariant normal form for nondegenerate singular orbits of integrable Hamiltonian systems

2003-02-24

arxiv.org/abs/math/0302287v4

Mathematics

Symplectic Geometry

21 pages, revised version, main changes in section 3

Scientific paper

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 non-degenerate orbit. We also show that the non-degeneracy condition is not equivalent to the non-resonance condition for smooth systems.

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