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...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/621312 |
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| _version_ | 1832551420343091200 |
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| author | Junyang Gao Gang Liu |
| author_facet | Junyang Gao Gang Liu |
| author_sort | Junyang Gao |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b24f665974474dc39eaf09b037eb799e |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-b24f665974474dc39eaf09b037eb799e2025-02-03T06:01:35ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/621312621312On Connectivity of Fatou Components concerning a Family of Rational MapsJunyang Gao0Gang Liu1School of Science, China University of Mining and Technology, Beijing 100083, ChinaDepartment of Mathematics and Computational Science, Hengyang Normal University, Hengyang 421002, ChinaI. 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.http://dx.doi.org/10.1155/2014/621312 |
| spellingShingle | Junyang Gao Gang Liu On Connectivity of Fatou Components concerning a Family of Rational Maps Abstract and Applied Analysis |
| title | On Connectivity of Fatou Components concerning a Family of Rational Maps |
| title_full | On Connectivity of Fatou Components concerning a Family of Rational Maps |
| title_fullStr | On Connectivity of Fatou Components concerning a Family of Rational Maps |
| title_full_unstemmed | On Connectivity of Fatou Components concerning a Family of Rational Maps |
| title_short | On Connectivity of Fatou Components concerning a Family of Rational Maps |
| title_sort | on connectivity of fatou components concerning a family of rational maps |
| url | http://dx.doi.org/10.1155/2014/621312 |
| work_keys_str_mv | AT junyanggao onconnectivityoffatoucomponentsconcerningafamilyofrationalmaps AT gangliu onconnectivityoffatoucomponentsconcerningafamilyofrationalmaps |