Dynamics of composite functions meromorphic outside a small set
Let M denote the class of functions f meromorphic outside some compact totally disconnected set E = E(f) and the cluster set of f at any a ∈ E with respect to Ec= ℂ̂\E is equal to ℂ̂. It is known that class M is closed under composition. Let f and g be two functions in class M, we study relationship...
Saved in:
| Main Authors: | , |
|---|---|
| 格式: | 雜誌 |
| 出版: |
2018
|
| 主題: | |
| 在線閱讀: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=16344384404&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/62293 |
| 標簽: |
添加標簽
沒有標簽, 成為第一個標記此記錄!
|
| 總結: | Let M denote the class of functions f meromorphic outside some compact totally disconnected set E = E(f) and the cluster set of f at any a ∈ E with respect to Ec= ℂ̂\E is equal to ℂ̂. It is known that class M is closed under composition. Let f and g be two functions in class M, we study relationship between dynamics of f o g and g o f. Denote by F(f) and J(f) the Fatou and Julia sets of f. Let U be a component of F(f o g) and V be a component of F(g o f) which contains g (U). We show that under certain conditions U is a wandering domain if and only if V is a wandering domain; if U is periodic, then so is V and moreover, V is of the same type according to the classification of periodic components as U unless U is a Siegel disk or Herman ring. © 2004 Elsevier Inc. All rights reserved. |
|---|