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We consider the system in the title where the initial condition We show that the system has exactly two prime period-5 solutions and a unique equilibrium point . 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.

On the Global Character of the System of Piecewise Linear Difference Equations xn+1=|xn|−yn−1 and yn+1=xn−|yn|