Geodesic
On Computing Linearizing Coordinates from the Symmetry Algebra
Sajid Ali1, 2 ; Hassan Azad3 ; Said Waqas Shah3 ; Fazal M. Mahomed4, 5
1Dept. of Mathematics and Statistics, College of Natural and Health Sciences, Zayed University, Dubai, UAE
2School of Electrical Engineering and Computer Science, National University of Sciences and Technology, Islamabad, Pakistan
3Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan
4DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences, School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, South Africa
5School of Mathematics and Statistics, University of New South Wales, Sydney, Australia
Journal of Lie Theory, Tome 31 (2021) no. 3, pp. 625-635

Voir la notice de l'article provenant de la source Heldermann Verlag

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

Sajid Ali  1 , 2   ; Hassan Azad  3   ; Said Waqas Shah  3   ; Fazal M. Mahomed  4 , 5

1 Dept. of Mathematics and Statistics, College of Natural and Health Sciences, Zayed University, Dubai, UAE
2 School of Electrical Engineering and Computer Science, National University of Sciences and Technology, Islamabad, Pakistan
3 Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan
4 DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences, School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, South Africa
5 School of Mathematics and Statistics, University of New South Wales, Sydney, Australia 
Sajid Ali; Hassan Azad; Said Waqas Shah; Fazal 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/JOLT_2021_31_3_a1/
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