16 February 2000.

Cathrine Vembre Jensen "Geometrical structures on the solution spaces of ordinary differential equations" (continuation).

We introduce the notion of the solution space of an integrable distribution on a manifold, as a quotient space of this manifold by the corresponding integral manifolds foliation. We investigate criteria for tensors to be invariant on our distribution. This will provide the algebraic framework in which we will place Cartan distributions of differential equations. We shall look at ODEs of order k (that can be resolved with respect  to the highest derivative), and especially the case k=2.

For k=2 we shall see examples of equations that possess (co-)symmetries, metric structure and symplectic structure, all in the sense of invariant tensors.