Simultaneous Approximation by Attracting Basins
Abstract
We show that any d≥3 pairwise-disjoint open sets A1, ..., Ad⊂C sharing a common boundary J can be simultaneously approximated by the d attracting basins A1, ..., Ad of a rational map r having Fatou set F(r)=A1...d and so that the Julia set J(r) approximates J.
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