Non-Autonomous Basins of Attraction With 4-Dimensional Boundaries

Details Non-Autonomous Basins of Attraction With 4-Dimensional Boundaries Non-Autonomous Basins of Attraction With 4-Dimensional Boundaries

2004-10-07

arxiv.org/abs/math/0410210v1

Mathematics

Complex Variables

15 pages

Scientific paper

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.

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