2006/02/28 by Denis Gaidashev, Gaidashev, Denis, Michael Yampolsky +1
Mathematics · #Advanced Algebra and Geometry #Analytic Number Theory Research #Mathematical Dynamics and Fractals #math.DS #msc:37F25
paper · pdf · doi:10.48550/arxiv.math/0603008
Revised version. To appear in Exp. Math
arxiv created 2006/08/03 · arxiv updated 2009/12/01
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 a convincing evidence to support the Hyperbolicity Conjecture in this setting.