Constructing Non-Computable Julia Sets

2006/04/17 by Mark Braverman, Braverman, Mark, Michael Yampolsky +1
Computer Science · Mathematics · #37F50 #Analytic Number Theory Research #Computability, Logic, AI Algorithms #Computational Complexity (cs.CC) #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.math/0604371

openalex publication_date 2006/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We completely characterize the conformal radii of Siegel disks in the family P_θ(z)=e^2πiθz+z², corresponding to \bf computable parameters θ. As a consequence, we constructively produce quadratic polynomials with \bf non-computable Julia sets.

Citations

• On the Complexity of Real Functions

Related

• On quadratic Siegel disks with a class of unbounded type rotation numbers
• Non-computable Julia sets
• Rigidity of bounded type cubic Siegel polynomials
• On the area rate of perturbed Siegel disks
• Computability of Julia sets