On Multiply Connected Wandering Domains of Meromorphic Functions
نویسندگان
چکیده
We describe conditions under which a multiply connected wandering domain of a transcendental meromorphic function with a finite number of poles must be a Baker wandering domain, and we discuss the possible eventual connectivity of Fatou components of transcendental meromorphic functions. We also show that if f is meromorphic, U is a bounded component of F (f) and V is the component of F (f) such that f(U) ⊂ V , then f maps each component of ∂U onto a component of the boundary of V in Ĉ. We give examples which show that our results are sharp; for example, we prove that a multiply connected wandering domain can map to a simply connected wandering domain, and vice versa.
منابع مشابه
On the Uniform Perfectness of the Boundary of Multiply Connected Wandering Domains
We investigate in which cases the boundary of a multiply connected wandering domain of an entire function is uniformly perfect. We give a general criterion implying that it is not uniformly perfect. This criterion applies in particular to examples of multiply connected wandering domains given by Baker. We also provide examples of infinitely connected wandering domains whose boundary is uniforml...
متن کاملAn Entire Function with Simply and Multiply Connected Wandering Domains
We modify a construction of Kisaka and Shishikura to show that there exists an entire function f which has both a simply connected and a multiply connected wandering domain. Moreover, these domains are contained in the set A(f) consisting of the points where the iterates of f tend to infinity fast. The results answer questions by Rippon and Stallard.
متن کاملNon-existence of Unbounded Fatou Components of a Meromorphic Function Zheng Jian-hua and Piyapong Niamsup
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 function. 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 leas...
متن کاملIteration of Meromorphic Functions
4. The Components of the Fatou set 4.1. The types of domains of normality 4.2. The classification of periodic components 4.3. The role of the singularities of the inverse function 4.4. The connectivity of the components of the Fatou set 4.5. Wandering domains 4.6. Classes of functions without wandering domains 4.7. Baker domains 4.8. Classes of functions without Baker domains 4.9. Completely in...
متن کاملA Riemann Surface Attached to Domains in the Plane and Complexity in Potential Theory
We prove that if either of the Bergman or Szegő kernel functions associated to a multiply connected domain Ω in the plane is an algebraic function, then there exists a compact Riemann surface R such that Ω is a domain in R and such that a long list of classical domain functions associated to Ω extend to R as single valued meromorphic functions. Because the field of meromorphic functions on a co...
متن کامل