Boundedness of Fatou Components of Holomorphic Maps |
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| Authors: | Chunlei Cao Yuefei Wang |
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| Institution: | (1) Department of Mathematics, School of Science, Beijing Institute of Technology, Beijing, 100080, P.R.China;(2) Insititute of Mathematics AMSS, Chinese Academy of Science, Beijing, 10080, P.R. China |
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| Abstract: | We shall discuss the topological properties of the Fatou sets for holomorphic maps. Let f
1,f
2,....,f
N
be non-constant holomorphic maps in the plane, each having order less than 1/2. It is shown that if the lower order of f
j
, is greater than 0 for some j {1,2,...,N}, then the Fatou set of the map h=f
N
 f
N-1 ... f
1 has no unbounded components |
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| Keywords: | Fatou set Julia set boundedness |
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