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math.DS2018
Area and Hausdorff dimension of Sierpiński carpet Julia sets
Yuming Fu, Fei Yang
We prove the existence of rational maps whose Julia sets are Sierpiński carpets having positive area. Such rational maps can be constructed such that they either contain a Cremer f…
math.DS2018
Quasisymmetric uniformization and Hausdorff dimensions of Cantor circle Julia sets
Weiyuan Qiu, Fei Yang
For Cantor circle Julia sets of hyperbolic rational maps, we prove that they are quasisymmetrically equivalent to standard Cantor circles (i.e., connected components are round circ…
math.DS2018
Cantor Julia sets with Hausdorff dimension two
Fei Yang
We prove the existence of Cantor Julia sets with Hausdorff dimension two. In particular, such examples can be found in cubic polynomials. The proof is based on the characterization…