Commentarii Mathematici Helvetici


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Volume 75, Issue 2, 2000, pp. 271–283
DOI: 10.1007/PL00000375

Published online: 2000-06-30

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

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 $ {\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.

Keywords: Integrable systems, torus actions, singularities

: A note on degenerate corank-one singularities of integrable Hamiltonian systems. Comment. Math. Helv. 75 (2000), 271-283. doi: 10.1007/PL00000375