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Repelling periodic points of given periods of rational functions

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Abstract

Let R(z) be a rational function of degree d ⩾ 2. Then R(z) has at least one repelling periodic point of given period k ⩾ 2, unless k = 4 and d = 2, or k = 3 and d ⩽ 3, or k = 2 and d ⩽ 8. Examples show that all exceptional cases occur.

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Authors and Affiliations

  1. Department of Mathematics, Changshu Institute of Technology, Changshu, 215500, China

    Chang Jianming

  2. Department of Applied Mathematics, South China Agricultural University, Guangzhou, 510642, China

    Fang Mingliang

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  1. Chang Jianming
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  2. Fang Mingliang
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Correspondence to Chang Jianming.

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Chang, J., Fang, M. Repelling periodic points of given periods of rational functions. SCI CHINA SER A 49, 1165–1174 (2006). https://doi.org/10.1007/s11425-006-2008-2

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  • DOI: https://doi.org/10.1007/s11425-006-2008-2

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