On Stronger Forms of Sensitivity in Non-autonomous Systems

In this paper, some stronger forms of transitivity in a non-autonomous discrete dynamical system (X, f1,∞) generated by a sequence (fn) of continuous self maps converging uniformly to f, are studied. The concepts of thick sensitivity, ergodic sensitivity and multi-sensitivity for non-autonomous discrete dynamical systems, which are all stronger forms of sensitivity, are defined and studied. It is proved that under certain conditions, if the rate of convergence at which (fn) converges to f is “sufficiently fast”, then various forms of sensitivity and transitivity for the non-autonomous system (X, f1,∞) and the autonomous system (X, f) coincide. Also counter examples are given to support results.