Periods of a max-type equation

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 $$\left\{N+m:m\ge 1,m\in \mathbb{N}\right\}\subset \mathrm{Per}(F_4).$$

39 pages, 1 figure; to be published in Journal of Difference Equations and Applications

References in corpus (1)

• The maximum of the complementary of a semigroup with restricted conditions