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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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Campoamor Stursberg, Otto Ruttwig (2012) Systems of second-order linear ODE’s with constant coefficients and their symmetries. II. The case of non-diagonal coefficient matrices. Communications in Nonlinear Science and Numerical Simulation, 17 (3). pp. 1178-1193. ISSN 1007-5704

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Official URL: http://www.sciencedirect.com/science/article/pii/S100757041100428X


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Abstract

We 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.


Item Type:Article
Uncontrolled Keywords:Lie group method; Point symmetry; Lie algebra; Levi factor; Linearization
Subjects:Sciences > Mathematics > Differential equations
ID Code:20787
Deposited On:12 Apr 2013 13:24
Last Modified:12 Dec 2018 15:12

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