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2007 Cylinder Renormalization of Siegel Disks
Denis Gaidashev, Michael Yampolsky
Experiment. Math. 16(2): 215-226 (2007).

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.

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Denis Gaidashev. Michael Yampolsky. "Cylinder Renormalization of Siegel Disks." Experiment. Math. 16 (2) 215 - 226, 2007.

Information

Published: 2007
First available in Project Euclid: 7 March 2008

zbMATH: 1145.37028
MathSciNet: MR2339277

Subjects:
Primary: 37F25
Secondary: 30C62

Keywords: Beltrami equation , Measurable Riemann Mapping Theorem , renormalization , Siegel disc , Universality

Rights: Copyright © 2007 A K Peters, Ltd.

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Vol.16 • No. 2 • 2007
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