The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Commentarii Mathematici Helvetici


Full-Text PDF (323 KB) | Metadata | Table of Contents | CMH summary
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