On Stronger Forms of Sensitivity in Non-autonomous Systems

Abstract

In this paper, some stronger forms of transitivity in a non-autonomous discrete dynamical system $(X,f_{1,\infty})$ generated by a sequence $(f_n)$ 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 $(f_n)$ converges to $f$ is “sufficiently fast”, then various forms of sensitivity and transitivity for the non-autonomous system $(X,f_{1,\infty})$ and the autonomous system $(X,f)$ coincide. Also counter examples are given to support results.