Lie's Reduction Method and Differential Galois Theory in the Complex Analytic Context

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dc.creatorBlázquez-Sanz, David
dc.creatorMorales-Ruiz, Juan José
dc.date2009-01-28
dc.date.accessioned2026-07-07T12:35:13Z
dc.date.available2026-07-07T12:35:13Z
dc.descriptionThis 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.
dc.description31 pages
dc.identifierhttps://arxiv.org/abs/0901.4479
dc.identifierhttp://arxiv.org/abs/0901.4479
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/217698
dc.subjectClassical Analysis and ODEs
dc.subjectComplex Variables
dc.subject34M05; 12H05; 14L99; 34A26
dc.titleLie's Reduction Method and Differential Galois Theory in the Complex Analytic Context
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