6 papers · 1 filter
On the formulas of meromorphic functions with periodic Herman rings
Fei Yang
We construct some explicit formulas of rational maps and transcendental meromorphic functions having Herman rings of period strictly larger than one. This gives an answer to a ques…
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…
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…
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…
A criterion to generate carpet Julia sets
Fei Yang
It was known that the Sierpiński carpets can appear as the Julia sets in the families of some rational maps. In this article we present a criterion that guarantees the existence of…
Singular perturbations with multiple poles of the simple polynomials
Yingqing Xiao, Fei Yang
In this article, we study the dynamics of the following family of rational maps with one parameter: \begin{equation*} f_λ(z)= z^n+\frac{λ^2}{z^n-λ}, \end{equation*} where …