Science in China Series A: Mathematics

, Volume 49, Issue 9, pp 1165–1174

Repelling periodic points of given periods of rational functions

Article

DOI: 10.1007/s11425-006-2008-2

Cite this article as:
Chang, J. & Fang, M. SCI CHINA SER A (2006) 49: 1165. doi:10.1007/s11425-006-2008-2
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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.

Keywords

rational function iterate fixed point periodic point repelling periodic point 

Copyright information

© Science in China Press 2006

Authors and Affiliations

  1. 1.Department of MathematicsChangshu Institute of TechnologyChangshuChina
  2. 2.Department of Applied MathematicsSouth China Agricultural UniversityGuangzhouChina

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