Abstract:

This paper deals with the system induced by the nonprimitive and nonconstantlength substitution ζ over the alphabet {0,1}, w
here  ζ(0)=0a₁…a_p-1, ζ(1)=1,…,1. It has been proved  that this system is LiYorke chaotic if and only if there exists i>0  such that a_i=0. In addition, investigating the occurrent frequency of the symbols shows a sufficient condition for the system not to be distributively chaotic.

Key words: substitution system, LiYorke chaos, distributional chaos