Shapes of polynomial Julia sets, revisited
Kathryn A. Lindsey

TL;DR
This paper demonstrates that any finite union of disjoint Jordan curves in the complex plane can be approximated arbitrarily closely by polynomial Julia sets, with a constructive proof provided.
Contribution
It provides a constructive method to approximate arbitrary finite unions of Jordan curves using polynomial Julia sets.
Findings
Finite unions of Jordan curves can be approximated by polynomial Julia sets
The approximation is arbitrarily close in the Hausdorff topology
The proof of approximation is constructive
Abstract
Any finite union of disjoint, mutually exterior Jordan curves in the complex plane can be approximated arbitrarily well in the Hausdorff topology by polynomial Julia sets. Furthermore, the proof is constructive.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Point processes and geometric inequalities · Mathematics and Applications
