Structure of the McMullen domain in the parameter planes for rational maps

• Autorzy: Robert L. Devaney
• Języki publikacji: EN

Abstrakty

EN

We show that, for the family of functions $F_{λ}(z) = zⁿ + λ/zⁿ$ where n ≥ 3 and λ ∈ ℂ, there is a unique McMullen domain in parameter space. A McMullen domain is a region where the Julia set of $F_{λ}$ is homeomorphic to a Cantor set of circles. We also prove that this McMullen domain is a simply connected region in the plane that is bounded by a simple closed curve.

Kategorie tematyczne

• 37F45: Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations
• 37F10: Polynomials; rational maps; entire and meromorphic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2005
• Tom: 185
• Numer: 3
• Strony: 267-285

Daty

wydano

2005

Twórcy

autor

Robert L. Devaney

• Boston University, Boston, MA 02215, U.S.A.

Identyfikatory

DOI

10.4064/fm185-3-5