  We consider two types of non-autonomous 2-periodic Gumovski-Mira difference
equations. We show that while the corresponding autonomous recurrences are
conjugated, the behavior of the sequences generated by the 2-periodic ones
differ dramatically: in one case the behavior of the sequences is simple
(integrable) and in the other case it is much more complicated (chaotic). We
also present a global study of the integrable case that includes which periods
appear for the recurrence.
