Relation of Some Chaos Characterizations on 1-Step Shift of Finite Type over Two Symbols

Abstract

A 1-step shift of finite type over two symbols is a collection of sequences over symbols 0 and 1 with some constraints. The constraints are identified by a set of forbidden blocks, which are not allowed to appear in any sequences in the space. The space is of finite type since the number of forbidden blocks is finite, and it is of 1-step type since the forbidden blocks are of the length of 2. On a 1-step shift of finite type over two symbols, the specification property, the almost specification property, and locally everywhere onto are the three chaotic characterizations that we look into in this study. We discovered that the specification property and the locally everywhere onto qualities are more important than Devaney chaos to demonstrate the chaotic behaviour of dynamical systems. However, almost specification property is weaker than Devaney chaos.