Geometrical aspects of integrable systems

Abstract

We review some basic theorems on integrability of Hamiltonian systems, namely the Liouville-Arnold theorem on complete integrability, the Nekhoroshev theorem on partial integrability and the Mishchenko-Fomenko theorem on noncommutative integrability, and for each of them we give a version suitable for the noncompact case. We give a possible global version of the previous local results, under certain topological hypotheses on the base space. It turns out that locally affine structures arise naturally in this setting.

It will appear on International Journal of Geometric Methods in Modern Physics vol.5 n.3 (May 2008) issue

References in corpus (5)

• The Poincare'-Lyapounov-Nekhoroshev theorem
• Bi-Hamiltonian partially integrable systems
• Global action-angle coordinates for completely integrable systems with noncompact invariant submanifolds
• Noncommutative integrability on noncompact invariant manifolds
• Geometric quantization of time-dependent completely integrable Hamiltonian systems