Non-existence of unbounded Fatou components of a meromorphic function

2007/11/20 by Zheng Jian-Hua, Jian-Hua, Zheng, Piyapong Niamsup +1
Mathematics · #30D05 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #math.CV #math.DS #msc:30D05

paper · pdf · doi:10.48550/arxiv.0711.3051

14 pages

arxiv created 2007/11/20 · arxiv updated 2009/12/01

Abstract

This paper is devoted to establish sufficient conditions under which a transcendental meromorphic function has no unbounded Fatou components and to extend some results for entire functions to meromorphic functions. Actually, we shall mainly discuss non-existence of unbounded wandering domains of a meromorphic function. The case for a composition of finitely many meromorphic function with at least one of them being transcendental can be also investigated in the argument of this paper.

Related

• Connectivity of Fatou Components of Meromorphic Functions
• Iterates of Meromorphic Functions on Escaping Fatou Components
• On Fatou sets containing Baker omitted value
• Dynamics on the Wandering Components of the Fatou Set of Three Transcendental Entire Functions and Their Composites
• Some results in the uniqueness of meromorphic function