Decreasing case on characteristic endpoints question for iterative roots of PM functions |
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| Authors: | Lin Li Liu Liu |
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| Affiliation: | 1. College of Mathematics, Physics and Information Engineering, Jiaxing University, Jiaxing, Zhejiang 314001, P.R. China;2. Department of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan 610031, P.R. China |
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| Abstract: | For PM functions of height 1, the existence of continuous iterative roots of any order was obtained under the characteristic endpoints condition. A natural open question about iterative roots without that condition was raised. This question was answered partially in the case that the function is increasing on its characteristic interval. In this paper, to the opposite, we consider the decreasing case and give the existence and nonexistence results for their iterative roots. |
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| Keywords: | Iterative root piecewise monotone function characteristic interval nonmonotonicity height characteristic endpoints condition |
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