Stable manifolds of automorphisms of at fixed points

Abstract

We study the stable manifolds of automorphisms F of at hyperbolic fixed points. If F(0)=0, we denote λ1,…,λn the all eigenvalues of the tangent map DF(0). If λ1,…,λn satisfy the condition (∗)(see Definition), we show that the stable manifold at point 0 is an injectively immersed complex sub manifold biholomorphically equivalent to C n-k , where F 1=F,F l-1 F 1=F and n−k is the cardinal number of the eigenvalues of DF(0) whose absolute values are less than 1.