3-Adic System and Chaos

Abstract

Let $\left(Z\right(3),\tau )$ be a 3-adic system. we prove in $\left(Z\right(3),\tau )$ the existence of uncountable distributional chaotic set of $A\left(\tau \right)$, which is an almost periodic points set, and further come to a conclusion that $\tau$ is chaotic in the sense of Devaney and Wiggins.