Geometrical aspects of integrable systems
Mathematical Physics
2015-05-13 v1 math.MP
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.
Cite
@article{arxiv.0802.1905,
title = {Geometrical aspects of integrable systems},
author = {Emanuele Fiorani},
journal= {arXiv preprint arXiv:0802.1905},
year = {2015}
}
Comments
It will appear on International Journal of Geometric Methods in Modern Physics vol.5 n.3 (May 2008) issue