On the global character of the system of piecewise linear difference equations x n+1 =|x n|- y n -1 and y n+1 = x n -|y n|

Abstract

We consider the system in the title where the initial condition (x 0, y 0) ∈ R 2. We show that the system has exactly two prime period-5 solutions and a unique equilibrium point (0, - 1). We also show that every solution of the system is eventually one of the two prime period-5 solutions or else the unique equilibrium point. Copyright © 2010 Wirot Tikjha et al.