The positive topological entropy not equivalent to chaos. A class of subshifts
Let \(X\) be a compact metric space and let \(f:X \to X\) be a continuous map. If \(x \neq y\) are points in \(X\) such that \(\limsup d(f^ n(x)\), \(f^ n(y))>0\) and \(\liminf d(f^ n(x), f^ n(y)) = 0\), then \(\{x,y\}\) is called a chaotic pair (for \(f)\). If \(X_ 0\) is an invariant subset of \(X\) which contains an uncountable subset \(D\) such that any two different points in \(D\) form a chaotic pair, then \(f\) is called chaotic on \(X_ 0\) [\textit{T.-Y. Li} and \textit{J. A. Yorke}, Am. Math. Mon. 82, 985-992 (1975; Zbl 0351.92021)]. In the paper under review the authors prove that every one-sided shift contains a chaotic minimal subshift with zero topological entropy.
scientific article; zbMATH DE number 700523