Dynamics of composite functions meromorphic outside a small set |
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Authors: | Keaitsuda Maneeruk |
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Institution: | Department of Mathematics, Faculty of Science, Chiangmai University, Chiangmai, 50200, Thailand |
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Abstract: | 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 is equal to . 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○g and g○f. Denote by F(f) and J(f) the Fatou and Julia sets of f. Let U be a component of F(f○g) and V be a component of F(g○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. |
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Keywords: | Functions meromorphic outside a small sets Wandering domain |
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