A Fatou type theorem for complex map germs

Leonardo Câmara, Bruno Scárdua
2012 Conformal Geometry and Dynamics  
In this paper we prove a Fatou type theorem for complex map germs. More precisely, we give (generic) conditions assuring the existence of parabolic curves for complex map germs tangent to the identity, in terms of existence of suitable formal separatrices. Such a map cannot have finite orbits.
doi:10.1090/s1088-4173-2012-00242-1 fatcat:vvzmpse64beinlr7tjk2aese34