The iteration of entire function (Q2732164)
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scientific article; zbMATH DE number 1623275
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The iteration of entire function |
scientific article; zbMATH DE number 1623275 |
Statements
13 May 2002
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entire function
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Julia set
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Fatou set
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growth
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order
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The iteration of entire function (English)
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Let \(f\) be a transcendental entire function. It is shown that if \(\log\log M(r,f)=O((\log r)^{\alpha})\) for some \(\alpha<1\), then all components of the Fatou set of \(f\) are bounded. The proof relies heavily on previous work by \textit{G. M. Stallard} [Math. Proc. Camb. Philos. Soc. 114, 43-55 (1993; Zbl 0782.30023)].
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