Geometric proof of Lie's linearization theorem
Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences2004 (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)
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.
Lie's linearization test, symmetries, linearizable equations, Lie group analysis, differential equations
IdentifiersURN: urn:nbn:se:bth-8850ISI: 000222611300005Local ID: oai:bth.se:forskinfo4A45CD66D886F7ACC12573BE005B70C5OAI: oai:DiVA.org:bth-8850DiVA: diva2:836605