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arXiv · 1903.11715

Classification of commutative pairs of surjective maps of interval, one of which is unimodal

Makar Plakhotnyk
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Abstract

We introduce here a classification of unimodal maps $[0, 1]\rightarrow [0, 1]$, which commute with piecewise linear surjective maps $[0, 1]\rightarrow [0, 1]$. Remind that if continuous piecewise linear unimodal map $g$ commutes with a non-constant piecewise linear map $\psi$, which is not an iteration of $g$, then $g$ is topologically conjugated with the tent map by piecewise linear conjugacy. We use the obtained classification to illustrate the mentioned fact.

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Makar Plakhotnyk. 2019-03-27. Classification of commutative pairs of surjective maps of interval, one of which is unimodal. https://arxiv.org/abs/1903.11715

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