Dynamics Of Finitely Generated Non-Autonomous Systems

In this paper, we discuss dynamical behavior of a non-autonomous system generated by a finite family $\mathbb{F}$. In the process, we relate the dynamical behavior of the non-autonomous system generated by the family $\mathbb{F}=\{f_1,f_2,\ldots,f_k\}$ with the dynamical behavior of the system $(X,f_k\circ f_{k-1}\circ\ldots\circ f_1)$. We discuss properties like minimality, equicontinuity, proximality and various forms of sensitivities for the two systems. We derive conditions under which the dynamical behavior of $(X,f_k\circ f_{k-1}\circ\ldots\circ f_1)$ is carried forward to $(X,\mathbb{F})$ (and vice-versa). We also give examples to illustrate the necessity of the conditions imposed.