On the global behavior of 𝑥ᵤ₊₁ = |𝑥ᵤ|− 𝑦ᵤ − 1 and 𝑦ᵤ₊₁ = 𝑥ᵤ +|𝑦ᵤ|
Author
Grove, E. A.
Lapierre, E.
Tikjha, W.
Full text
https://revistas.ufro.cl/ojs/index.php/cubo/article/view/134510.4067/S0719-06462012000200007
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.