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math.DS2008★ 3 cited
Period Doubling in Area-Preserving Maps: An Associated One Dimensional Problem
Denis Gaidashev, Hans Koch
It has been observed that the famous Feigenbaum-Coullet-Tresser period doubling universality has a counterpart for area-preserving maps of $\field{R}^2$. A renormalization approach…
math.DS2006
Cylinder renormalization of Siegel disks
Denis Gaidashev, Michael Yampolsky
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 prob…
math.DS2005
Cylinder renormalization for Siegel disks and a constructive Measurable Riemann Mapping Theorem
Denis G. Gaidashev
The boundary of the Siegel disk of a quadratic polynomial with an irrationally indifferent fixed point with the golden mean rotation number has been observed to be self-similar. Th…