Global behavior of the max-type difference equation \(x_{n+1}=\max\{1/x_{n},A_{n}/x_{n - 1}\}\)
Summary: We study global behavior of the following max-type difference equation \(x_{n+1}=\max\{1/x_{n},A_{n}/x_{n - 1}\}, n=0,1,\dots,\) where \(\{A_n\}_{n=0}^{\infty}\) is a sequence of positive real numbers with \(0\leq \text{inf} A_{n}\leq \text{sup} A_{n}<1\). The special case when \(\{A_n\}_{n=0}^{\infty}\) is a periodic sequence with period \(k\) and \(A_{n}\in (0,1)\) for every \(n\geq 0\) has been completely investigated by \textit{Y. Chen} [J. Difference Equ. Appl. 11, No.~15, 1289--1294 (2005; Zbl 1086.39003)]. Here, we extend his results to the general case.
scientific article; zbMATH DE number 5574409