Non-existence of Unbounded Fatou Components of a Meromorphic Function Zheng Jian-hua and Piyapong Niamsup

Iteration of certain meromorphic functions with unbounded singular values

Let M= { f (z)= (zm/sinhm z) for z ∈ C | either m or m/2 is an odd natural number}. For each f ∈M, the set of singularities of the inverse function of f is an unbounded subset of the real line R. In this paper, the iteration of functions in oneparameter family S = { fλ(z)= λ f (z) | λ ∈ R \ {0}} is investigated for each f ∈M. It is shown that, for each f ∈M, there is a critical parameter λ > 0 ...

Dynamics of Newton’s Functions of Barna’s Polynomials

Functions of Small Growth with No Unbounded Fatou Components

We prove a form of the cosπρ theorem which gives strong estimates for the minimum modulus of a transcendental entire function of order zero. We also prove a generalisation of a result of Hinkkanen that gives a sufficient condition for a transcendental entire function to have no unbounded Fatou components. These two results enable us to show that there is a large class of entire functions of ord...

Uniqueness of meromorphic functions dealing with multiple values in an angular domain

This paper uses the Tsuji’s characteristic to investigate the uniqueness of transcen- dental meromorphic function with shared values in an angular domain dealing with the multiple values which improve a result of J. Zheng.

Meromorphic Functions with Two Completely Invariant Domains

We show that if a meromorphic function has two completely invariant Fatou components and only finitely many critical and asymptotic values, then its Julia set is a Jordan curve. However, even if both domains are attracting basins, the Julia set need not be a quasicircle. We also show that all critical and asymptotic values are contained in the two completely invariant components. This need not ...