Singularities of second-order implicit differential equations: A geometrical approach (Q1868366)

The author studies the singularities of implicit second-order ordinary differential equations. The article begins with a brief review of results on the first-order case. Then, the type of singularities considered by the author are introduced and the behaviour of the equation in their neighbourhood is analysed for the simplest cases. The used approach is based on a natural completion of the jet spaces \(J^1(\mathbb{R},\mathbb{R})\) and \(J^2(\mathbb{R},\mathbb{R})\) allowing the derivatives to become infinite.