Constructing Non-Computable Julia Sets

Abstract

We completely characterize the conformal radii of Siegel disks in the family $$P_{\theta }(z)=e^{2\pi i\theta }z+z^2,$$ corresponding to {\bf computable} parameters $\theta$. As a consequence, we constructively produce quadratic polynomials with {\bf non-computable} Julia sets.

References in corpus (2)

• On the Complexity of Real Functions
• Filled Julia sets with empty interior are computable