Recurrence of the Limit System under Uniform Convergence

This paper discusses the relationships of the recurrent set between the dynamical systems sequence and the limit system under uniform convergence.In the first place,it obtains the relationships of the fixed points set and the chain recurrent points set between the dynamical systems sequence and the limit system under uniform convergence;second,the relationships of the regularly recurrent points set(quasi)weakly almost periodic points set and non-wandering points set between the dynamical systems sequence and the limit system under the definition are given.