Filled Julia sets with empty interior are computable
I. Binder, M. Braverman, M. Yampolsky
TL;DR
This paper proves that polynomial filled Julia sets with empty interior can be computed algorithmically, advancing understanding of their computational properties.
Contribution
It establishes the computability of filled Julia sets with empty interior, a previously unresolved question in complex dynamics.
Findings
Filled Julia sets with empty interior are computable.
The result applies to a broad class of polynomial Julia sets.
This advances the theory of computability in complex dynamics.
Abstract
We show that if a polynomial filled Julia set has empty interior, then it is computable.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Computability, Logic, AI Algorithms · Advanced Topology and Set Theory