Sur les Théorèmes I et II de Painlevé

Frank Loray (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We lecture on fundamental Painleve's early Theoremson first order ordinary differential equations with manyexamples. We end-up with two conjectures aboutthe global analytic continuation of holonomy mapslocally defined by Theorem II.

Mots clés: équations différentielles ordinaires; points singuliers mobiles; prolongement analytique

Domaines: Analyse classique [math.CA]; Variables complexes [math.CV]

Frank Loray. Sur les Théorèmes I et II de Painlevé. Geometry and Dynamics, International conference in honnour of the 60th Anniversary of Alberto Verjovsky, 2005, Cuernavaca, Mexico. pp.165--190. ⟨hal-00001191⟩