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Lie point symmetries for systems of second order linear ordinary differential equations. (English) Zbl 0649.34018
Recently it was shown that some nonlinear second order differential equations could be linearized by a point transformation generated by the generator G=τ/t+η/x, where τ=τ(x,t), η=η(x,t) are unknown coefficients. Because the set of all generators of a differential equation creates a Lie algebra under the operation of the Lie bracket it is interest in finding the number of generators for a system of differential equations. The paper in the heading deals with the mentioned problem for the system x '' =ax+by, y '' =cx+dy, where a,b,c,d are constant coefficients. Some considerations are extended to higher dimensional systems. The case when a,b,c,d depend upon t is also discussed.
Reviewer: J.Banás
MSC:
34A30Linear ODE and systems, general
22E60Lie algebras of Lie groups
17B15Representations of Lie algebras, analytic theory