%0 Journal Article
%T On two and three periodic Lyness difference equations
%A Anna Cima
%A Armengol Gasull
%A Victor Manosa
%J Mathematics
%D 2009
%I arXiv
%R 10.1080/10236198.2010.524212
%X We describe the sequences {x_n}_n given by the non-autonomous second order Lyness difference equations x_{n+2}=(a_n+x_{n+1})/x_n, where {a_n}_n is either a 2-periodic or a 3-periodic sequence of positive values and the initial conditions x_1,x_2 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.
%U http://arxiv.org/abs/0912.5031v1