Abstract

We study non-autonomous Lyness type recurrences of the form $x_{n+2}=(a_n+x_n)/x_{n+1}$, where ${a_n}_n$ is a $k$-periodic sequence of positive numbers with prime period $k$. We show that for the cases $kin{1,2,3,6}$ the behaviour of the sequence ${x_n}_n$ is simple (integrable) while for the remaining cases satisfying $k e5$ this behaviour can be much more complicated (perturbed twist map). The cases $k=5$ are studied separately.

The talk is based on a joint work with A. Cima and V. Mañosa