Integrability and non-integrability of periodic non-autonomous Lyness recurrences

Anna Cima, Armengol Gasull, Víctor Mañosa

This paper studies non-autonomous Lyness type recurrences of the form $x_{n+2}=(a_n+x_{n+1})/x_n$, where $\{a_n\}$ is a $k$-periodic sequence of positive numbers with primitive p…