11-107 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) Aug 2, 11

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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.

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