Quasi-homogénéité des applications holomorphes propres d’un domaine quasi-disqué sur un domaine disqué

A result of F. Berteloot and G.Patrizio [1] states that if f is a proper holomorphic map between two bounded complete circular domains Ω1 and Ω2 in C n+1 (n≥1), such that f -1 {0}={0} and such that the principal part fp of the Taylor expansions of f at the origin is nondegenerated i.e fp -1 {0}={0}, then f≡fp . Here we propose to generalize their result in the case where Ω1 is a complete quasi-circular domain and Ω2 is a complete circular domain. Moreover this proof does not use the tools of projective dynamics of J. E. Fornaess and N. Sibony [3].