Differential Galois Theory and Lie Symmetries
Classical Analysis and ODEs
2015-11-23 v3 Differential Geometry
Dynamical Systems
Abstract
We study the interplay between the differential Galois group and the Lie algebra of infinitesimal symmetries of systems of linear differential equations. We show that some symmetries can be seen as solutions of a hierarchy of linear differential systems. We show that the existence of rational symmetries constrains the differential Galois group in the system in a way that depends of the Maclaurin series of the symmetry along the zero solution.
Keywords
Cite
@article{arxiv.1503.09023,
title = {Differential Galois Theory and Lie Symmetries},
author = {David Blázquez-Sanz and Juan J. Morales-Ruiz and Jacques-Arthur Weil},
journal= {arXiv preprint arXiv:1503.09023},
year = {2015}
}