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arXiv · 1808.03622

Piecewise linear unimodal maps with non-trivial continuous piecewise linear commutator

Makar Plakhotnyk
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Abstract

Let $g:\, [0, 1]\rightarrow [0, 1]$ be piecewise linear unimodal map. We say that $g$ has non-trivial piecewise linear commutator, if there is a continuous piecewise linear $\psi:\, [0, 1]\rightarrow [0, 1]$ such that $g\circ \psi = \psi\circ g$, and, moreover, $\psi$ is neither an iteration of $g$, not a constant map. We prove that if $g$ has a non-trivial piecewise linear commutator, then $g$ is topologically conjugated with the tent map by a piecewise linear conjugacy.

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Makar Plakhotnyk. 2018-08-10. Piecewise linear unimodal maps with non-trivial continuous piecewise linear commutator. https://arxiv.org/abs/1808.03622

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