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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Fekete polynomials and shapes of Julia sets


Authors: Kathryn A. Lindsey and Malik Younsi
Journal: Trans. Amer. Math. Soc. 371 (2019), 8489-8511
MSC (2010): Primary 30E10, 37F10; Secondary 30C85
DOI: https://doi.org/10.1090/tran/7440
Published electronically: March 28, 2019
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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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Additional Information

Kathryn A. Lindsey
Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
Email: klindsey@math.uchicago.edu

Malik Younsi
Affiliation: Department of Mathematics, Stony Brook University, Stony Brook, New York 11794-3651
Email: malik.younsi@gmail.com

DOI: https://doi.org/10.1090/tran/7440
Keywords: Fekete points, polynomials, Julia sets, Hausdorff distance, Leja points
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
Article copyright: © Copyright 2019 American Mathematical Society