Systems of second-order linear ODE’s with constant coefficients and their symmetries. II. The case of non-diagonal coefficient matrices.

Campoamor Stursberg, Otto-Rudwig2023-06-202023-06-2020121007-570410.1016/j.cnsns.2011.08.002https://hdl.handle.net/20.500.14352/43748We complete the analysis of the symmetry algebra 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 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.engSystems of second-order linear ODE’s with constant coefficients and their symmetries. II. The case of non-diagonal coefficient matrices.journal articlehttps//doi.org/10.1016/j.cnsns.2011.08.002http://www.sciencedirect.com/science/article/pii/S100757041100428Xrestricted access517.9Lie group methodPoint symmetryLie algebraLevi factorLinearizationEcuaciones diferenciales1202.07 Ecuaciones en Diferencias