Systems of second-order linear ODE’s with constant coefficients and their symmetries

Starting from the study of the symmetries of systems of 4 second-order linear ODEs with constant real coefficients, we determine the dimension and generators of the symmetry algebra for systems of n equations described by a diagonal Jordan canonical form. We further prove that some dimensions between the lower and upper bounds cannot be attained in the diagonal case, and classify the Levi factors of the symmetry algebras.

Research highlights
► Symmetries of systems of second order linear ODE’s with constants coefficients.
► Analysis of possible dimensions.
► Symmetry algebras for general diagonal systems.
► Structure of Levi factors of symmetry algebras.