Dynamics of a family of rational maps concerning renormalization transformation

Abstract

Considering a family of rational maps T_{n\lambda }concerning renormalization transformation, we give a perfect description about the dynamical properties of T_{n\lambda } and the topological properties of the Fatou components F (T_{n\lambda }). Furthermore, we discuss the continuity of the Hausdorff dimension HD(J (T_{n\lambda })) about real parameter λ.

Keywords

Completely invariant domain / quasi-circle / Hausdorff dimension / renormalization transformation

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