Fekete polynomials and shapes of Julia sets

Lindsey, Kathryn; Younsi, Malik

doi:10.1090/tran/7440

Fekete polynomials and shapes of Julia sets
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by Kathryn A. Lindsey and Malik Younsi PDF

Trans. Amer. Math. Soc. 371 (2019), 8489-8511 Request permission

Abstract:

We prove that a nonempty, proper subset $S$ of the complex plane can be approximated in a strong sense by polynomial filled Julia sets if and only if $S$ is bounded and $\hat {\mathbb {C}} \setminus \textrm {int}(S)$ is connected. The proof that such a set is approximable by filled Julia sets is constructive and relies on Fekete polynomials. Illustrative examples are presented. We also prove an estimate for the rate of approximation in terms of geometric and potential theoretic quantities.

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