A criterion and constructions are given for Cantor bubble Julia sets in rational maps with attracting or parabolic fixed points, including high-period cycles, Hausdorff dimension two, and a quasisymmetric equivalence condition to round bubbles.
Roesch, On capture zones for the family f_ (z)=z^2+ /z^2 , Dynamics on the R iemann sphere, Eur
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Rational maps with Cantor bubble Julia sets
A criterion and constructions are given for Cantor bubble Julia sets in rational maps with attracting or parabolic fixed points, including high-period cycles, Hausdorff dimension two, and a quasisymmetric equivalence condition to round bubbles.