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On the solutions of a max-type difference equation system. (English) Zbl 1335.39019
Summary: In this paper, we study the behavior of the solution of the following max-type difference equation system: \[ x_{n+1} = \max \left\{ \frac{1}{x_n}, \min\left\{1, \frac{A}{y_n}\right\}\right\}, \quad y_{n+1} = \max \left\{ \frac{1}{y_n}, \min\left\{1, \frac{A}{x_n}\right\}\right\}, \, n \in \mathbb N_0, \] where \(\mathbb N = \mathbb N \cup \{0\}\), the parameter \(A\) is a positive real number, and the initial values \(x_{0},y_{0}\) are positive real numbers.

MSC:
39A20 Multiplicative and other generalized difference equations, e.g., of Lyness type
39A23 Periodic solutions of difference equations
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