Relation between locally everywhere onto and the strong dense periodicity property on shift of finite type

Abstract

Transitivity and dense periodic points are two ingredients for Devaney chaos. It is well known that the two properties does not imply each other. In this paper, we investigate two stronger properties which are stronger than transitivity and dense periodic points, respectively. The properties are locally everywhere onto (l.e.o) and Pn dense for all n. We will show that the property of l.e.o implies the strong dense periodicity property (Pn dense for all n) on shift of finite type. Some examples will be given to show that this is not the case for other general spaces.