Periodic solutions of the Lyness max equation

We investigate the periodic nature of solutions of a “max-type” difference equation sometimes referred to as the “Lyness max” equation. The equation we consider is xn+1 = max{xn,A}/xn−1, n = 0, 1, . . ., where A is a positive real parameter and the initial conditions are arbitrary positive numbers. We also present related results for a similar equation sometimes referred to as the “period 7 max” equation.  2003 Elsevier Inc. All rights reserved.