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Journal of Lie Theory 31 (2021), No. 3, 625--635
Copyright Heldermann Verlag 2021

On Computing Linearizing Coordinates from the Symmetry Algebra

Sajid Ali
Dept. of Mathematics and Statistics, College of Natural and Health Sciences, Zayed University, Dubai, UAE
and: School of Electrical Engineering and Computer Science, National University of Sciences and Technology, Islamabad, Pakistan

Hassan Azad
Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan

Said Waqas Shah
Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan

Fazal M. Mahomed
DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences, School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, South Africa
and: School of Mathematics and Statistics, University of New South Wales, Sydney, Australia

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.

Keywords: Ordinary differential equations, linearization, vector fields, Lie algebras.

MSC: 34A26, 37C10, 57R30.

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