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4 papers · 2 filters
Mating non-renormalizable quadratic polynomials
Magnus Aspenberg, Michael Yampolsky
In this paper we prove the existence and uniqueness of matings of the basilica with any quadratic polynomial which lies outside of the 1/2-limb of M, is non-renormalizable, and doe…
Smooth linearization of commuting circle diffeomorphisms
Bassam Fayad, Kostantin Khanin
We show that a finite number of commuting diffeomorphisms with simultaneously Diophantine rotation numbers are smoothly conjugated to roations.
Constructing Non-Computable Julia Sets
Mark Braverman, Michael Yampolsky
We completely characterize the conformal radii of Siegel disks in the family corresponding to {\bf computable} parameters . As a consequence, we constr…
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…