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.References
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Additional Information
- Kathryn A. Lindsey
- Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
- MR Author ID: 842785
- Email: klindsey@math.uchicago.edu
- Malik Younsi
- Affiliation: Department of Mathematics, Stony Brook University, Stony Brook, New York 11794-3651
- MR Author ID: 1036614
- Email: malik.younsi@gmail.com
- Received by editor(s): September 21, 2017
- Received by editor(s) in revised form: October 11, 2017, and October 16, 2017
- Published electronically: March 28, 2019
- Additional Notes: The first author was supported by an NSF Mathematical Sciences Research Postdoctoral Fellowship
The second author was supported by NSERC and NSF Grant DMS-1664807 - © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 8489-8511
- MSC (2010): Primary 30E10, 37F10; Secondary 30C85
- DOI: https://doi.org/10.1090/tran/7440
- MathSciNet review: 3955554