MERCREDI 18 NOVEMBRE 2009
14 heures
Salle Séminaire 5
Centre de Physique Théorique
Marseille-Luminy

Mikhail Babich
Institut Euler, St Petersburg, Russie

Title: Projective Structure of the Painlevé equations

Abstract: The talk is devoted to the equivalence problem for the
Painlev\'e equations. I will talk about the Theory of Invariants of
the ODE's, and about the difficulties that arise when the theory is
applied to the Painlev\'e equations. To avoid the obstacle we consider
the E. Cartan's theory of the Spaces with the Normal Projective
Connection. The application of the theory to the Painlev\'e equations
makes possible to define a nice geometrical object --- the surfaces,
immersed to P^3 in a special way. The equivalence class of equations
transformable to a Painleve equation uniquelly corresponds to such a
surface.