Global behaviour of solutions of cyclic systems of q order 2 or 3 generalized Lyness' difference equations and of other more general equations of higher order

Abstract

We study the global behaviour of the solutions of cyclic systems of q order k difference equations with q unknown sequences . If σ denotes the direct cyclic permutation , such a system is: for values of k and choices of f which correspond, first to cases of classical simple difference equations : order 2 or 3 extended Lyness' equations, order 2 generalized Lyness' type equations associated to conics, or to elliptic cubics or quartics; and then with f which becomes from other more general order k equations.