arXiv math/03022872003-02math.SGmath.DS

Equivariant normal form for nondegenerate singular orbits of integrable Hamiltonian systems

Eva Miranda, Nguyen Tien Zung

备注：: 21 pages, revised version, main changes in section 3
发表信息：: Ann. Sci. Ecole Norm. Sup.,37 (2004), no. 6, 819--839

英文摘要：

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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