Non-Autonomous Basins of Attraction With 4-Dimensional Boundaries

2004/10/07 by Han Peters, Erlend Fornæss Wold, Peters, Han +1 · 1 citation
Earth and Planetary Sciences · Mathematics · #Geology and Paleoclimatology Research #Geometry and complex manifolds #Marine and environmental studies #math.CV #msc:32H02 #msc:32H50

paper · pdf · doi:10.48550/arxiv.math/0410210

15 pages

arxiv created 2004/10/07 · arxiv updated 2009/12/01

Abstract

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

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