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Geometric proof of Lie's linearization theorem
Ansvarig organisation
2004 (Engelska)Ingår i: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 36, nr 1, s. 41-46Artikel i tidskrift (Refereegranskat) PublishedAlternativ titel
Geometric proof of Lie's linearization theorem (Svenska)
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.

Ort, förlag, år, upplaga, sidor
Dordrecht: Springer , 2004. Vol. 36, nr 1, s. 41-46
Nyckelord [en]
Lie's linearization test, symmetries, linearizable equations, Lie group analysis, differential equations
Nationell ämneskategori
Matematisk analys
Identifikatorer
URN: urn:nbn:se:bth-8850ISI: 000222611300005Lokalt ID: oai:bth.se:forskinfo4A45CD66D886F7ACC12573BE005B70C5OAI: oai:DiVA.org:bth-8850DiVA, id: diva2:836605
Tillgänglig från: 2012-09-18 Skapad: 2007-12-27 Senast uppdaterad: 2017-12-04Bibliografiskt granskad

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