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Non-Autonomous basins of attraction and their boundaries

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Abstract

We study whether the basin of attraction of a sequence of automorphisms of ℂk is biholomorphic to ℂk. In particular, we show that given any sequence of automorphisms with the same attracting fixed point, the basin is biholomorphic to ℂk, if every map is iterated sufficiently many times. We also construct Fatou-Bieberbach domains in ℂ2 whose boundaries are four-dimensional.

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Authors and Affiliations

  1. Mathematics Department, University of Michigan, 48109, Ann Arbor, MI

    Han Peters & Erlend Fornœss Wold

  2. Mathematics Department, University of Oslo, Blindern NO-0316, PO-Box 1053, Oslo, Norway

    Han Peters & Erlend Fornœss Wold

Authors
  1. Han Peters
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  2. Erlend Fornœss Wold
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Communicated by Steven G. Krantz

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Peters, H., Wold, E.F. Non-Autonomous basins of attraction and their boundaries. J Geom Anal 15, 123–136 (2005). https://doi.org/10.1007/BF02921861

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  • DOI: https://doi.org/10.1007/BF02921861

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