Science China Mathematics

, Volume 53, Issue 3, pp 593–596 | Cite as

Normal families and fixed points of iterates



Let \( \mathcal{F} \) be a family of holomorphic functions and suppose that there exists ɛ > 0 such that if f\( \mathcal{F} \), then |(f 2)′(ξ)| ⩽ 4 − ɛ for all fixed points ξ of the second iterate f 2. We show that then \( \mathcal{F} \) is normal. This is deduced from a result which says that if p is a polynomial of degree at least 2, then p 2 has a fixed point ξ such that |(p 2)′(ξ)| ⩾ 4. The results are motivated by a problem posed by Yang Lo.


fixed point multiplier normality iteration periodic point 


Primary 30D45 Secondary 30D05, 37F10 


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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Mathematisches Seminar der Christian-Albrechts-Universität zu KielKielGermany

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