On the Set of Periods of the 2-Periodic Lyness’ Equation

Abstract

We study the periodic solutions of the non-autonomous periodic Lyness' recurrence u n+2 = (a n + u n+1 )/u n , where {a n } n is a cycle with positive values a,b and with positive initial conditions. Among other methodological issues we give an outline of the proof of the following results: (1)