Non-computable Julia sets
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Publication:5469247
DOI10.1090/S0894-0347-05-00516-3zbMath1099.37042OpenAlexW1809268447WikidataQ122998317 ScholiaQ122998317MaRDI QIDQ5469247
Michael Yampolsky, Mark Braverman
Publication date: 17 May 2006
Published in: Journal of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0894-0347-05-00516-3
Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) (68Q17)
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Cites Work
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- Siegel disks with smooth boundaries
- Filled Julia sets with empty interior are computable
- On computational complexity of Siegel Julia sets
- The Brjuno functions and their regularity properties
- Variation of the conformal radius
- On the Julia set of a typical quadratic polynomial with a Siegel disk
- Iteration of analytic functions
- Computable functionals
- The computational complexity of some julia sets
- On the dynamics of polynomial-like mappings
- Frontiers in complex dynamics
- COMPLEXITY AND REAL COMPUTATION: A MANIFESTO
- Parabolic Julia sets are polynomial time computable
- On Computable Numbers, with an Application to the Entscheidungsproblem