R. Campoamor-Stursberg
Systems of second-order linear ODE's with constant coefficients and their symmetries II. The case of non-diagonal coefficient matrices
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ABSTRACT. We complete the analysis of the symmetry algebra $\mathcal{L}$ for
systems of $n$ second-order linear ODEs with constant real
coefficients, by studying the case of coefficient matrices having
a non-diagonal Jordan canonical form. We also classify the Levi
factor (maximal semisimple subalgebra) of $\mathcal{L}$, showing
that it is completely determined by the Jordan form. A universal
formula for the dimension of the symmetry algebra of such systems
is given. As application, the case $n=5$ is analyzed.