Experimental Mathematics

Cylinder Renormalization of Siegel Disks

Denis Gaidashev and Michael Yampolsky

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Abstract

We study one of the central open questions in one-dimensional renormalization theory---the conjectural universality of golden-mean Siegel disks. We present an approach to the problem based on cylinder renormalization proposed by the second author. Numerical implementation of this approach relies on the constructive measurable Riemann mapping theorem proved by the first author. Our numerical study yields convincing evidence to support the hyperbolicity conjecture in this setting.

Article information

Source
Experiment. Math., Volume 16, Issue 2 (2007), 215-226.

Dates
First available in Project Euclid: 7 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.em/1204905877

Mathematical Reviews number (MathSciNet)
MR2339277

Zentralblatt MATH identifier
1145.37028

Subjects
Primary: 37F25: Renormalization
Secondary: 30C62: Quasiconformal mappings in the plane

Keywords
Siegel disc renormalization universality Beltrami equation Measurable Riemann Mapping Theorem

Citation

Gaidashev, Denis; Yampolsky, Michael. Cylinder Renormalization of Siegel Disks. Experiment. Math. 16 (2007), no. 2, 215--226. https://projecteuclid.org/euclid.em/1204905877


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