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THE AKIYAMA MEAN-MEDIAN MAP HAS UNBOUNDED TRANSIT TIME AND DISCONTINUOUS LIMIT
Published online by Cambridge University Press: 23 November 2022
Abstract
Open conjectures state that, for every $x\in [0,1]$, the orbit $(x_n)_{n=1}^\infty $ of the mean-median recursion
with initial data $(x_1,x_2,x_3)=(0,x,1)$, is eventually constant, and that its transit time and limit functions (of x) are unbounded and continuous, respectively. In this paper, we prove that for the slightly modified recursion
first suggested by Akiyama, the transit time function is unbounded but the limit function is discontinuous.
Keywords
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 108 , Issue 2 , October 2023 , pp. 298 - 307
- Copyright
- © The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.