2009/01/28 by David Blázquez-Sanz, Blázquez-Sanz, David, Juan José Morales-Ruiz +1
Mathematics · Physics and Astronomy · #12H05 #14L99 #34A26 #34M05 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.0901.4479
openalex publication_date 2009/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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 more general class of differential equations adimitting superposition laws, as recently stated in [5]. A Lie-Vessiot sys- tem is automatically translated into a equation in a Lie group that we call automorphic system. Reciprocally an automorphic system induces a hierarchy of Lie-Vessiot systems. In this work we study the global analytic aspects of a classical method of reduction of differential equations, due to S. Lie. We propose an differential Galois theory for automorphic systems, and explore the relationship between integrability in terms of Galois the- ory and the Lie's reduction method. Finally we explore the algebra of Lie symmetries of a general automorphic system.