A note on degenerate corank-one singularities of integrable Hamiltonian systems
Nguyen Tien Zung
Université de Montpellier II, France
![A note on degenerate corank-one singularities of integrable Hamiltonian systems cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserials%2Fcover-cmh.png&w=3840&q=90)
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 -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.
Cite this article
Nguyen Tien Zung, 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