Linearizing Systems of Second-Order ODEs via Symmetry Generators Spanning a Simple Subalgebra |
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| Authors: | R Campoamor-Stursberg J Guerón |
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| Institution: | 1. Dpto de Geometría y Topología and IMI, Fac. CC. Mat. UCM, Plaza de Ciencias 3, 28040, Madrid, Spain
2. Instituto de Astronomía y Física del Espacio, CC 67 sucursal 26, 1428, Buenos Aires, Republic of Argentina
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| Abstract: | It is shown that a system of n second order ordinary differential equations that possess 2(n?1) symmetries of certain type necessarily has maximal symmetry $\frak{sl}(n+2,\mathbb{R})$ . Further, it is shown for non-linearizable systems containing a subalgebra of symmetries isomorphic to $\frak{sl}(n-1,\mathbb{R})$ the dimension of the symmetry algebra $\mathcal{L}$ is d≥n 2?1. Examples showing that the upper bound is sharp are given. |
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