Dynamical behavior of a general non-autonomous dynamical system

In this work, we investigate dynamical notions such as minimality, almost periodicity, equicontinuity, transitivity, proximality and periodicity for a general non-autonomous dynamical system. We provide necessary and sufficient conditions for a non-autonomous system to be minimal. We prove that for an equicontinuous system (X,F), if x is almost periodic then OH(x) is uniformly almost periodic. We also establish preservance of almost periodicity under uniform convergence. We also establish some results capturing the qualitative behavior of a general non-autonomous dynamical system.