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Geometric proof of Lie's linearization theorem
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2004 (English)In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 36, no 1, 41-46 p.Article in journal (Refereed) PublishedAlternative title
Geometric proof of Lie's linearization theorem (Swedish)
Abstract [en]

S. Lie found in 1883 the general form of all second-order ordinary differential equations transformable to the linear equation by a change of variables and proved that their solution reduces to integration of a linear third-order ordinary differential equation. He showed that the linearizable equations are at most cubic in the first-order derivative and described a general procedure for constructing linearizing transformations by using an over-determined system of four equations. We present here a simple geometric proof of the theorem, known as Lie's linearization test, stating that the compatibility of Lie's four auxiliary equations furnishes a necessary and sufficient condition for linearization.

Place, publisher, year, edition, pages
Dordrecht: Springer , 2004. Vol. 36, no 1, 41-46 p.
Keyword [en]
Lie's linearization test, symmetries, linearizable equations, Lie group analysis, differential equations
National Category
Mathematical Analysis
URN: urn:nbn:se:bth-8850ISI: 000222611300005Local ID: diva2:836605
Available from: 2012-09-18 Created: 2007-12-27 Last updated: 2015-06-30Bibliographically approved

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