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Repelling periodic points of given periods of rational functions |
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| Authors: | |
| Institution: | 1. Department of Mathematics, Changshu Institute of Technology, Changshu 215500, China 2. Department of Applied Mathematics, South China Agricultural University, Guangzhou 510642, China |
| 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 |
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