Normal families and fixed points of iterates
Complex Variables
2010-04-02 v1 Dynamical Systems
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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Cite
@article{arxiv.1001.4511,
title = {Normal families and fixed points of iterates},
author = {Walter Bergweiler},
journal= {arXiv preprint arXiv:1001.4511},
year = {2010}
}
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5 pages