Exponential Dichotomies, Almost Periodic Structurally Stable Differential Systems, and an ExampleU

In this paper, we introduce concepts of almost periodic topological in short, APT.equivalence and almost periodic structural in short, APS. stability of differential systems, and a necessary and sufficient condition for APS stability of differential systems. Furthermore, we discuss the inheritability of the APS stability and density of APS stable differential systems in a certain space of uniformly almost periodic differential systems