Attracting domains of maps tangent to the identity whose only characteristic direction is non-degenerate

Abstract

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.

References in corpus (1)

• Basins of attraction of automorphisms in C^3

Cited by in corpus (2)

• Domain of attraction for maps tangent to the identity in ${\mathbb{C}}^2$ with characteristic direction of higher degree
• Dynamics of quasi-parabolic one-resonant biholomorphisms