Revisiting Lie integrability by quadratures from a geometric perspective
Mathematical Physics
2017-01-17 v1 Classical Analysis and ODEs
math.MP
Exactly Solvable and Integrable Systems
Abstract
After a short review of the classical Lie theorem, a finite dimensional Lie algebra of vector fields is considered and the most general conditions under which the integral curves of one of the fields can be obtained by quadratures in a prescribed way will be discussed, determining also the number of quadratures needed to integrate the system. The theory will be illustrated with examples andbn an extension of the theorem where the Lie algebras are replaced by some distributions will also be presented.
Cite
@article{arxiv.1701.03907,
title = {Revisiting Lie integrability by quadratures from a geometric perspective},
author = {José F. Cariñena and Fernando Falceto and Janusz Grabowski and Manuel F. Rañada},
journal= {arXiv preprint arXiv:1701.03907},
year = {2017}
}
Comments
14 pages, proceedings of the conference "50th Seminar Sophus Lie", 25 September - 1 October 2016, Bedlewo, Poland