Recurrence in non-autonomous dynamical systems

We consider a sequence f1,∞={f1,f2,f3,…} of continuous maps on a compact metric space X uniformly converging to a function f. This sequence forms a non-autonomous discrete dynamical system. In such case, the set of omega-limit points is invariant with respect to the limit function f. Here we give negative answer to questions whether the sets of recurrent points and non-wandering points are also invariant. We also discuss the relation of the set of recurrent points of f1,∞ and its limit function f.