Attracting domains of maps tangent to the identity whose only   characteristic direction is non-degenerate
  We prove that a holomorphic fixed point germ in two complex variables, tangent to the identity, and whose only characteristic direction is non-degenerate, has a domain of attraction on which the map is conjugate to a translation. In the case of a global automorphism, the corresponding domain of attraction is a Fatou-Bieberbach domain. 
Sara Lapan
math.DS math.CV