Deforming Lie algebras to Frobenius integrable non-autonomous Hamiltonian systems
Exactly Solvable and Integrable Systems
2021-07-09 v4 Mathematical Physics
math.MP
Abstract
Motivated by the theory of Painlev\'e 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-St\"ackel systems.
Keywords
Cite
@article{arxiv.1712.08155,
title = {Deforming Lie algebras to Frobenius integrable non-autonomous Hamiltonian systems},
author = {Maciej Blaszak and Krzysztof Marciniak and Artur Sergyeyev},
journal= {arXiv preprint arXiv:1712.08155},
year = {2021}
}
Comments
14 pages, no figures. We repaired Example 5 and also made some minor amendments in the text