On dynamics generated by a uniformly convergent sequence of maps

In this paper, we investigate the dynamics of a non-autonomous dynamical system (X,F) generated by a uniformly convergent sequence of continuous self maps on X. We relate the dynamical behavior of (X,F) with the dynamical behavior of the limiting system (and vice versa). In the process, we relate properties like equicontinuity, minimality, various forms of mixing and sensitivities, dense periodicity and denseness of proximal pairs (cells) for the two systems. We also give examples to investigate the necessity of the conditions imposed.