The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-662-52927-0_22

We study the periodic solutions of the non-autonomous periodic Lyness’ recurrence un+2=(an+un+1)/un, where {an}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) If (a,b)¿(1,1), then there exists a value p0(a,b) such that for any p>p0(a,b) there exist continua of initial conditions giving rise to 2p-periodic sequences. (2) The set of minimal periods arising when (a,b)¿(0,8)2 and positive initial conditions are considered, contains all the even numbers except 4, 6, 8, 12 and 20. If a¿b, then it does not appear any odd period, except 1.

Peer Reviewed