Constructing non-computable Julia sets

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Conference object 11 Jun 2007Embargo end date: 01 Jan 2006Publisher:ACMJournal:Proceedings of the thirty-ninth annual ACM symposium on Theory of computing

Authors: Mark Braverman; Michael Yampolsky;

doi: 10.1145/1250790.1250893 , 10.48550/arxiv.math/0604371

arXiv: math/0604371

Constructing non-computable Julia sets

- Summary
- Subjects
- Metrics

Abstract

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

Related Organizations

University of Toronto
Canada

Keywords

FOS: Computer and information sciences, Computer Science - Computational Complexity, 37F50, FOS: Mathematics, Dynamical Systems (math.DS), Mathematics - Dynamical Systems, Computational Complexity (cs.CC)

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	14
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Top 10%
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average