Some pinching deformations of the Fatou function

• Autorzy: Patricia Domínguez , Guillermo Sienra
• Języki publikacji: EN

Abstrakty

EN

We are interested in deformations of Baker domains by a pinching process in curves. In this paper we deform the Fatou function $F(z) = z + 1 + e^{-z}$, depending on the curves selected, to any map of the form $F_{p/q}(z) = z + e^{-z} + 2πip/q$, p/q a rational number. This process deforms a function with a doubly parabolic Baker domain into a function with an infinite number of doubly parabolic periodic Baker domains if p = 0, otherwise to a function with wandering domains. Finally, we show that certain attracting domains can be deformed by a pinching process into doubly parabolic Baker domains.

Kategorie tematyczne

• 37D05: Hyperbolic orbits and sets
• 37F10: Polynomials; rational maps; entire and meromorphic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2015
• Tom: 228
• Numer: 1
• Strony: 1-15

Daty

wydano

2015

Twórcy

autor

Patricia Domínguez

• Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Puebla, Mexico

autor

Guillermo Sienra

• Departamento de Matemáticas, Facultad de Ciencias, UNAM, México, D.F., Mexico

Identyfikatory

DOI

10.4064/fm228-1-1