Existence of non-algebraic singularities of differential equation

Yohann Genzmer (1) , Loïc Teyssier (1)

1 IRMA - Institut de Recherche Mathématique Avancée

An algebraizable singularity is a germ of a singular holomorphic foliation which can be defined in some appropriate local chart by a differential equation with algebraic coefficients. We show that there exists at least countably many saddle-node singularities of the complex plane that are not algebraizable.

Mots clés: algebraic differential equation; singularity of foliation

Domaines: Systèmes dynamiques [math.DS]

Yohann Genzmer, Loïc Teyssier. Existence of non-algebraic singularities of differential equation. Journal of Differential Equations, 2010, 248 (5), pp.1256-1267. ⟨10.1016/j.jde.2009.10.001⟩. ⟨hal-00362002v2⟩