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Equivariant normal form for nondegenerate singular orbits of integrable Hamiltonian systems

Eva Miranda·Nguyen Tien Zung
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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 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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Eva Miranda, Nguyen Tien Zung. 2004-07-30. Equivariant normal form for nondegenerate singular orbits of integrable Hamiltonian systems. https://arxiv.org/abs/math/0302287

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