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math.DS1998
Mating Siegel Quadratic Polynomials
Michael Yampolsky, Saeed Zakeri
Let F be a quadratic rational map of the sphere which has two fixed Siegel disks with bounded type rotation numbers theta and nu. Using a new degree 3 Blaschke product model for th…
math.DS1998
The Attractor of Renormalization and Rigidity of Towers of Critical Circle Maps
Michael Yampolsky
We demonstrate the existence of a global attractor A with a Cantor set structure for the renormalization of critical circle mappings. The set A is invariant under a generalized ren…