JournalscmhVol. 75 , No. 2DOI 10.1007/pl00000375

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

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

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.