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Differential Galois Theory and Lie Symmetries
David Blázquez-Sanz, Juan J. Morales-Ruiz, Jacques-Arthur Weil
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 symmetri…
Differential Galois Theory of Algebraic Lie-Vessiot Systems
David Blázquez-Sanz, Juan José Morales-Ruiz
In this paper we develop a differential Galois theory for algebraic Lie-Vessiot systems in algebraic homogeneous spaces. Lie-Vessiot systems are non autonomous vector fields that a…
Lie's Reduction Method and Differential Galois Theory in the Complex Analytic Context
David Blázquez-Sanz, Juan José Morales-Ruiz
This paper is dedicated to the differential Galois theory in the complex analytic context for Lie-Vessiot systems. Those are the natural generaliza- tion of linear systems, and the…
Local and Global Aspects of Lie's Superposition Theorem
David Blázquez-Sanz, Juan José Morales-Ruiz
In this paper we give the global conditions for an ordinary differential equation to admit a superposition law of solutions in the classical sense. This completes the well-known Li…