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arXiv · 2111.01651

Periods of a max-type equation

Antonio Linero Bas·Daniel Nieves Roldán
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Abstract

We consider the max-type equation $$x_{n+4}=\max\{x_{n+3},x_{n+2},x_{n+1},0\}-x_n,$$ with arbitrary real initial conditions. We describe completely its set of periods $\mathrm{Per}(F_4)$, as well as its associate periodic orbits. We also prove that there exists a natural number $N\notin\mathrm{Per}(F_4)$ for which $$\left\{N+m:m\geq 1,m\in\mathbb N\right\}\subset\mathrm{Per}(F_4).$$

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Antonio Linero Bas, Daniel Nieves Roldán. 2021-11-02. Periods of a max-type equation. https://doi.org/10.1080/10236198.2021.2000971

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