We show that the map T(x,y)=( y,max(A,y)/x) is topologically conjugate to a family of rotation maps with rotation angle depending on the radius and easily computed. We exhibit an explicit isomorphism that allows us to find the solutions of the difference equation x_n+1=max(A,x_n)/x_n-1, x₀>0, x₁>0. We also prove a conjecture proposed in the reference [E. J. Janowski, V. L. Kocic, G. Ladas and S. W. Schultz, Global behavior of solutions of x _{n +1}=maxx _n,A /x _{n -1}, Proceedings of the First International Conference on Difference Equations, Trinity University, San Antonio, TX, 1994, pp. 273-282], completing the determination of the periodic points of T.