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arXiv · 1806.10184

Geometrical Properties of the Mean-Median Map

Jonathan Hoseana·Franco Vivaldi
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Abstract

We study the mean-median map as a dynamical system on the space of finite sets of piecewise-affine continuous functions with rational coefficients. We determine the structure of the limit function in the neighbourhood of a distinctive family of rational points, the local minima. By constructing a simpler map which represents the dynamics in such neighbourhoods, we extend the results of Cellarosi and Munday (arXiv:1408.3454v1 [math.CO]) by two orders of magnitude. Based on these computations, we conjecture that the Hausdorff dimension of the graph of the limit function of the set $[0,x,1]$ is greater than 1.

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Jonathan Hoseana, Franco Vivaldi. 2018-06-26. Geometrical Properties of the Mean-Median Map. https://arxiv.org/abs/1806.10184

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