Constructing locally connected non-computable Julia sets

DOI10.1007/s00220-009-0858-5zbMath1190.37050OpenAlexW2026688161WikidataQ121100388 ScholiaQ121100388MaRDI QIDQ1048108

Mark Braverman, Michael Yampolsky

Publication date: 11 January 2010

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00220-009-0858-5

zbMATH Keywords

quadratic polynomialJulia setSiegel diskcomputabilitylocally connected

Mathematics Subject Classification ID

Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Renormalization of holomorphic dynamical systems (37F25)

Related Items (7)

Computability of topological pressure on compact shift spaces beyond finite type* ⋮ Computability of the Julia set. Nonrecurrent critical orbits ⋮ On computational complexity of Cremer Julia sets ⋮ Almost every real quadratic polynomial has a poly-time computable Julia set ⋮ On the computability of rotation sets and their entropies ⋮ Non-computable impressions of computable external rays of quadratic polynomials ⋮ Computable Geometric Complex Analysis and Complex Dynamics

Cites Work

• The Brjuno function continuously estimates the size of quadratic Siegel disks
• Computability of Julia sets
• Filled Julia sets with empty interior are computable
• Are there critical points on the boundaries of singular domains?
• The Brjuno functions and their regularity properties
• Local connectivity of some Julia sets containing a circle with an irrational rotation
• Hyperbolicity of renormalization of critical circle maps
• On the Julia set of a typical quadratic polynomial with a Siegel disk
• Rigidity of critical circle mappings. I
• Quadratic Julia sets with positive Lebesgue measure.
• The dynamics of rational transforms: the topological picture
• Complex bounds for renormalization of critical circle maps
• Mating Siegel quadratic polynomials
• Non-computable Julia sets
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Constructing locally connected non-computable Julia sets