Geodesic
On Computing Linearizing Coordinates from the Symmetry Algebra
Journal of Lie theory, Tome 31 (2021) no. 3, pp. 625-635
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A characterization of the symmetry algebra of the Nth-order ordinary differential equations (ODEs) with maximal symmetry and all third-order linearizable ODEs is given. This is used to show that such an algebra g determines -- up to a point transformation -- only one linear equation whose symmetry algebra is g and an algorithmic procedure is given to find the linearizing coordinates. This procedure is applied to several examples from the literature.
Classification : 34A26, 37C10, 57R30
Mots-clés : Ordinary differential equations, linearization, vector fields, Lie algebras 
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     title = {On {Computing} {Linearizing} {Coordinates} from the {Symmetry} {Algebra}},
     journal = {Journal of Lie theory},
     pages = {625--635},
     year = {2021},
     volume = {31},
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S. Ali; H. Azad; S. W. Shah; F. M. Mahomed. On Computing Linearizing Coordinates from the Symmetry Algebra. Journal of Lie theory, Tome 31 (2021) no. 3, pp. 625-635. http://geodesic.mathdoc.fr/item/JLT_2021_31_3_JLT_2021_31_3_a1/