Une preuve de l'irréductibilité de l'équation de Painlevé II

par Jacques-Arthur Weil (XLIM-DMI)

jeudi 24 oct. 2013, 10:30 → 11:30 Europe/Paris

XR.203 (Bâtiment XLIM)

This is a joint work with Guy Casale. In his work on the first Painlevé equation, Guy Casale gave a characterization of the reducibility of non linear differential equations using Malgrange pseudogroup methods and classifications of E. Cartan. In our joint work, we propose an irreducibility criterion for second order non linear differential equations, based on the dimension of their Malgrange pseudogroup. We give a method to measure lower bounds on this dimension ; as an illustration, I will give a nice detailed proof of the irreducibility of the Painlevé II equation using this technique.