In this paper we consider the system of piecewise linear difference equations in the title, where the initial conditions x0 and y0 are real numbers. We show that there exists a unique equilibrium solution and exactly two prime period-3 solutions, and that except for the unique equilibrium solution, every solution of the system is eventually one of the two prime period-3 solutions.
@article{1345,
title = {On the global behavior of x+1 = |x|- y - 1 and y+1 = x +|y|},
journal = {CUBO, A Mathematical Journal},
volume = {14},
year = {2012},
language = {en},
url = {http://dml.mathdoc.fr/item/1345}
}
Grove, E.A.; Lapierre, E.; Tikjha, W. On the global behavior of 𝑥ᵤ₊₁ = |𝑥ᵤ|− 𝑦ᵤ − 1 and 𝑦ᵤ₊₁ = 𝑥ᵤ +|𝑦ᵤ|. CUBO, A Mathematical Journal, Tome 14 (2012) . http://gdmltest.u-ga.fr/item/1345/