On multiply-connected Fatou components in iteration of meromorphic functions ✩

By Jian-Hua Zheng. 2006

56 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/181a8a34a457ad02e47b78c4878a83c1094d05b4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Walter Bergweiler
2. G. Stallard
3. P. Rippon
4. Lasse Rempe

In Geometry and Topology

1. Walter Bergweiler
2. G. Stallard
3. P. Rippon
4. Lasse Rempe

In Mathematical Physics

1. Walter Bergweiler
2. G. Stallard
3. P. Rippon
4. Lasse Rempe

Citations in the corpus

• Multiply connected wandering domains of entire functions (2011, background): “ndental meromorphic functions with a direct tract; see [14] for the definition and properties of a function with a direct tract. As a first step, we note that a version of Theorem A was proved by Zheng [49] under the assumption that f is a transcendental meromorphic function with finitely many poles an”
• Slow escaping points of meromorphic functions (2008, background): “ch is a contradiction. Thus we deduce that if r > R0, then f (A(αr,βr)) covers at least one of the annuli A(α′R,β′R) or A(α′′R,β′′R), as required. We also require the following result due to Zheng [37]. SLOW ESCAPING POINTS 17 Lemma9.Let f be a transcendental meromorphic function with at most fini”
• Fast escaping points of entire functions (2010, unknown): “, for n∈ N. Hence, by Lemma 2.4, fn+N+1(U) ∩ {z: |z| <Mn(R/2)} = ∅, for n∈ N, so fN+1(U) ⊂ A R/2(f) as required. Alternatively, Theorem 4.4 can be proved by using the following result due to Zheng [54]. Lemma 4.5. Let f be a transcendental entire function. If f has a multiply connected Fatou comp”