On the obstruction to linearizability of 2-order ordinary differential equations

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dc.creatorYumaguzhin, Valeriy A.
dc.date2008-04-02
dc.date2008-04-03
dc.date.accessioned2026-07-07T09:29:51Z
dc.date.available2026-07-07T09:29:51Z
dc.descriptionIn this paper, we investigate the action of pseudogroup of all point transformations on the natural bundle of equations $y'' = u^0(x,y) + u^1(x,y)y' + u^2(x,y)(y')^2 + u^3(x,y)(y')^3$. We calculate the 1-st nontrivial differential invariant of this action. It is a horizontal differential 2-form with values in some algebra, it is defined on the bundle of 2--jets of sections of the considered bundle. We prove that this form is a unique obstruction to linearizability of these equations by point transformations.
dc.description14 pages; Ams-LateX 2e
dc.identifierhttps://arxiv.org/abs/0804.0306
dc.identifierhttp://arxiv.org/abs/0804.0306
dc.identifierActa Applicandae Mathematicae, Vol. 83, No. 1-2, 2004. pp.133-148
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/157938
dc.subjectDifferential Geometry
dc.subjectClassical Analysis and ODEs
dc.subject53A55; 53C10; 53C15; 34A30; 34A26; 34C20; 58F35
dc.titleOn the obstruction to linearizability of 2-order ordinary differential equations
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