Global stable manifolds in holomorphic dynamics under bunching   conditions
  We prove that the stable manifold of every point in a compact hyperbolic invariant set of a holomorphic automorphism of a complex manifold is biholomorphic to a complex vector space, provided that a bunching condition, which is weaker than the classical bunching condition for linearizability, holds. 
Alberto Abbondandolo and Pietro Majer
math.DS math.CV