Deforming Lie algebras to Frobenius integrable non-autonomous Hamiltonian systems
arXiv:1712.08155 · doi:10.1016/S0034-4877(21)00028-8
Abstract
Motivated by the theory of Painlevé equations and associated hierarchies, we study non-autonomous Hamiltonian systems that are Frobenius integrable. We establish sufficient conditions under which a given finite-dimensional Lie algebra of Hamiltonian vector fields can be deformed to a time-dependent Lie algebra of Frobenius integrable vector fields spanning the same distribution as the original algebra. The results are applied to quasi-Stäckel systems.
14 pages, no figures. We repaired Example 5 and also made some minor amendments in the text