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,…,λ_n the all eigenvalues of the tangent map DF(0). If λ₁,…,λ_n 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.

AMS No:

• 32H99
• 58F99