Evelyne Hubert: "Resolvent representation of differentially triangular systems"
INRIA, Sophia Antipolis, France

It is now well known that a system of n linear first order ordinary differential equations is equivalent to a single differential equation of order n. We shall expose a generalisation to nonlinear differential systems.

A polynomial differential system is equivalent to a finite set of differentially triangular systems (or differential characteristic sets). This set can be computed effectively by recent algorithms based on differential algebra and implemented in Maple. We show that the solution set of such a differentially triangular system is birationnally equivalent to the general solution of a single differential equation. We give an algorithm to compute this equation and the expression of the equivalence.