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arXiv · 1001.4511

Normal families and fixed points of iterates

Walter Bergweiler
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Abstract

Let F be a family of holomorphic functions and let K be a constant less than 4. Suppose that for all f in F the second iterate of f does not have fixed points for which the modulus of the multiplier is greater than K. We show that then F is normal. This is deduced from a result about the multipliers of iterated polynomials.

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Walter Bergweiler. 2010-01-25. Normal families and fixed points of iterates. https://doi.org/10.1007/s11425-010-0021-y

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