Non-Autonomous Basins of Attraction With 4-Dimensional Boundaries

Abstract

We study whether the basin of attraction of a sequence of automorphisms of ${\mathbb{C}}^k$ is biholomorphic to ${\mathbb{C}}^k$. In particular we show that given any sequence of automorphisms with the same attracting fixed point, the basin is biholomorphic to ${\mathbb{C}}^k$ if the maps are repeated often enough. We also construct Fatou-Bieberbach domains whose boundaries are 4-dimensional.

15 pages

References in corpus (1)

• Fatou-Bieberbach Domains

Cited by in corpus (1)

• Perturbed Basins of Attraction