Science in China Series A: Mathematics

, Volume 49, Issue 9, pp 1165-1174

First online:

Repelling periodic points of given periods of rational functions

  • Chang Jianming Affiliated withDepartment of Mathematics, Changshu Institute of Technology Email author 
  • , Fang Mingliang Affiliated withDepartment of Applied Mathematics, South China Agricultural University

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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.


rational function iterate fixed point periodic point repelling periodic point