On Connectivity of Fatou Components concerning a Family of Rational Maps
I. N. Baker established the existence of Fatou component with any given finite connectivity by the method of quasi-conformal surgery. M. Shishikura suggested giving an explicit rational map which has a Fatou component with finite connectivity greater than 2. In this paper, considering a family of ra...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/621312 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | I. N. Baker established the existence of Fatou component with any given finite connectivity by the method of quasi-conformal surgery. M. Shishikura suggested giving an explicit rational map which has a Fatou component with finite connectivity greater than 2. In this paper, considering a family of rational maps Rz,t that A. F. Beardon proposed, we prove that Rz,t has Fatou components with connectivities 3 and 5 for any t∈0,1/12. Furthermore, there exists t∈0,1/12 such that Rz,t has Fatou components with connectivity nine. |
|---|---|
| ISSN: | 1085-3375 1687-0409 |