A note on double minimality (Q2343041)

Let \(X\) be a compact metric space and \(T:X\to X\) be a homeomorphism. The following are the main results of this paper. { Theorem.} Under the precise context, we have {\parindent=6mm \begin{itemize} \item[i)] If \((X,T)\) is non-periodic and doubly minimal, then \((X,T)\) is not positively 2-rigid \item [ii)] If \((X,T)\) is doubly minimal, then \((X,T)\) is expansive; hence, a subshift. \end{itemize}} As a combination of these facts, the authors prove that any POD system is either uniformly rigid or a subshift.