Rational maps whose Julia sets are Cantor circles

Abstract

In this paper, we give a family of rational maps whose Julia sets are Cantor circles and show that every rational map whose Julia set is a Cantor set of circles must be topologically conjugate to one map in this family on their corresponding Julia sets. In particular, we give the specific expressions of some rational maps whose Julia sets are Cantor circles, but they are not topologically conjugate to any McMullen maps on their Julia sets. Moreover, some non-hyperbolic rational maps whose Julia sets are Cantor circles are also constructed.

28 pages, 6 figures; To appear in Ergod. Th. & Dynam. Sys

Cited by in corpus (5)

• Quasisymmetric geometry of the Julia sets of McMullen maps
• On hyperbolic rational maps with finitely connected Fatou sets
• Quasisymmetric uniformization and Hausdorff dimensions of Cantor circle Julia sets
• Julia sets as buried Julia components
• Singular perturbations with multiple poles of the simple polynomials