Differential invariants of 2--order ODEs, I

Abstract

In this paper, we investigate the action of pseudogroup of all point transformations on the natural bundle of equations $y^{\prime \prime }=a^3(x,y)(y^{\prime }{)}^3+a^2(x,y)(y^{\prime }{)}^2+a^1(x,y)y^{\prime }+a^0(x,y)$. We construct differential invariants of this action and solve the equivalence problem for some classes of these equations in particular for generic equations.

31 pages

References in corpus (1)

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

Cited by in corpus (1)

• On the obstruction to integrability of almost-complex structures