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Fekete polynomials and shapes of Julia sets
- Source :
- Transactions of the American Mathematical Society. 371:8489-8511
- Publication Year :
- 2019
- Publisher :
- American Mathematical Society (AMS), 2019.
-
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.
- Subjects :
- Polynomial
Mathematics::Complex Variables
Applied Mathematics
General Mathematics
010102 general mathematics
010103 numerical & computational mathematics
01 natural sciences
Constructive
Julia set
Set (abstract data type)
Combinatorics
Hausdorff distance
Rate of approximation
Bounded function
0101 mathematics
Complex plane
Mathematics
Subjects
Details
- ISSN :
- 10886850 and 00029947
- Volume :
- 371
- Database :
- OpenAIRE
- Journal :
- Transactions of the American Mathematical Society
- Accession number :
- edsair.doi...........fd34c4aa4154196d3b156632872e40f4