A difference equation with eventually periodic solutions

We show that every solution of the difference equation x(n+1) = max{1/x(n), A/x(n-1)}, n = 0, 1, ..., where the parameter A and the initial conditions x(-1) and x(0) are nonzero real numbers is eventually periodic with period 2, 3, or 4. We also give a precise description of the period in terms of A and the initial conditions. (C) 1998 Elsevier Science Ltd. All rights reserved.