4 citations · 12 across the 14 of their papers we have counts for
6 papers · 1 filter
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…
Computability of Julia sets
Mark Braverman, Michael Yampolsky
In this paper we settle most of the open questions on algorithmic computability of Julia sets. In particular, we present an algorithm for constructing quadratics whose Julia sets a…
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…
On computability of Julia sets: answers to questions of Milnor and Shub
Mark Braverman, Michael Yampolsky
In this note we give answers to questions posed to us by J.Milnor and M.Shub, which shed further light on the structure of non-computable Julia sets.
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…
Siegel disks and renormalization fixed points
Michael Yampolsky
In this note we construct hyperbolic fixed points for cylinder renormalization of maps with Siegel disks.