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...
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| Main Authors: | , |
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| Format: | Journal |
| Published: |
2018
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| Subjects: | |
| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=16344384404&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/62293 |
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| Institution: | Chiang Mai University |
| Summary: | 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. |
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