R. Campoamor-Stursberg
Systems of second-order linear ODE's with constant coefficients and their symmetries II. The case of non-diagonal coefficient matrices
(534K, pdf)

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.