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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 \(G=\tau \partial /\partial t+\eta \partial /\partial x,\) where \(\tau =\tau (x,t)\), \(\eta =\eta (x,t)\) 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:

34A30 Linear ordinary differential equations and systems
22E60 Lie algebras of Lie groups
17B15 Representations of Lie algebras and Lie superalgebras, analytic theory
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