On a strong dense periodicity property of shifts of finite type

There are various definitions of chaotic dynamical systems. The most utilized definition of chaos is Devaney chaos which isolates three components as being the essential features of chaos; transitivity, dense periodic points and sensitive dependence on initial conditions. In this paper, we focus on a strong dense periodicity property i.e. the set of points with prime period at least n is dense for each n. On shift of finite type over two symbols Σ₂, we show that the strong dense periodicity property implies another strong chaotic notions; locally everywhere onto (also called exact) and totally transitive