On the global behavior of 𝑥ᵤ₊₁ = |𝑥ᵤ|− 𝑦ᵤ − 1 and 𝑦ᵤ₊₁ = 𝑥ᵤ +|𝑦ᵤ|

Abstract

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.