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

Abstract

In this paper, we investigate the action of pseudogroup of all point transformations on the natural bundle of equations $y^{\prime \prime }=u^0(x,y)+u^1(x,y)y^{\prime }+u^2(x,y)(y^{\prime }{)}^2+u^3(x,y)(y^{\prime }{)}^3$. 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.

arXiv comment14 pages; Ams-LateX 2e

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