On a three-dimensional solvable system of difference equations

Abstract

In this paper we solve the following system of difference equations${mathcal x}_{n+1=;frac{z_{n-1}}{a+by_nz_{n-1}}}$ , ${mathcal y}_{n+1=;frac{{mathcal x}_{n-1}}{a+bz_n{mathcal x}_{n-1}}}$ , $z_{n+1=;frac{{mathcal y}_{n-1}}{a+b{mathcal x}_n{mathcal y}_{n-1}}}$ n ∈ $ {mathbb{N}}_0$ where parameters a, b and initial values ${mathcal x}_{-1;},;{mathcal x}_{0;},;{mathcal y}_{-1},;{mathcal y}_0,;z_{-1},;z_0 $ are nonzero real numbers, and give a representationof its general solution in terms of a specially chosen solutions to homogeneous linear difference equation with constantcoefficients associated to the system.