El títol de la versió pre-print de l'article és: On two and three periodic Lyness difference equations

Agraïments: GSD-UAB and CoDALab Groups are supported by the Government of Catalonia through the SGR program. They are also supported by through grants (first and second authors) and DPI2008-06699-C02-02 (third author).

We describe the sequences {xn}n given by the non-autonomous second order Lyness difference equations xn+2 = (an + xn+1)/xn, where {an}n is either a 2-periodic or a 3-periodic sequence of positive values and the initial conditions x1, x2 are as well positive. We also show an interesting phenomenon of the discrete dynamical systems associated to some of these difference equations: the existence of one oscillation of their associated rotation number functions. This behavior does not appear for the autonomous Lyness difference equations.