Perturbed Basins of Attraction

Mathematics – Complex Variables

Scientific paper

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11 pages

Scientific paper

Let F be an automorphism of C^k which has a fixed point. It is well known
that the basin of attraction is biholomorphically equivalent to C^k. We will
show that the basin of attraction of a sequence of automorphisms is also
biholomorphic to C^k if all the automorphisms are small perturbations of the
original map F.

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