JournalscmhVol. 75, No. 2pp. 271–283

A note on degenerate corank-one singularities of integrable Hamiltonian systems

A note on degenerate corank-one singularities of integrable Hamiltonian systems cover
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Abstract

We prove that, in a neighborhood of a corank-1 singularity of an analytic integrable Hamiltonian system with n degrees of freedom, there is a locally-free analytic symplectic Tn1{\Bbb T}^{n-1} -action which preserves the moment map, under some mild conditions. This result allows one to classify generic degenerate corank-one singularities of integrable Hamiltonian systems. It can also be applied to the study of (non)integrability of perturbations of integrable systems.

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, A note on degenerate corank-one singularities of integrable Hamiltonian systems. Comment. Math. Helv. 75 (2000), no. 2, pp. 271–283

DOI 10.1007/PL00000375