Differential Galois Theory and Lie Symmetries
Copyright policy )Differential Galois Theory and Lie Symmetries
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.
- University of Limoges France
- Universidad Politécnica de Madrid Spain
- National University of Colombia Colombia
- Université de Limoges France
- Complutense University of Madrid Spain
Mathematics - Differential Geometry, Geometric methods in ordinary differential equations, Picard-Vessiot theory, [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], Dynamical Systems (math.DS), Differential algebra, infinitesimal symmetries, Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain, differential Galois theory, Differential Geometry (math.DG), Mathematics - Classical Analysis and ODEs, 12H05, 34M15, 34A26, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Mathematics - Dynamical Systems, linear differential system
Mathematics - Differential Geometry, Geometric methods in ordinary differential equations, Picard-Vessiot theory, [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], Dynamical Systems (math.DS), Differential algebra, infinitesimal symmetries, Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain, differential Galois theory, Differential Geometry (math.DG), Mathematics - Classical Analysis and ODEs, 12H05, 34M15, 34A26, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Mathematics - Dynamical Systems, linear differential system
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