Hausdorff dimension of a chaotic set of shift of a symbolic space
The main result: Let \(\sigma\) be the shift on the space \(\Sigma_N\) of \(N\) symbols. Then there is a set \(A\subset \Sigma_N\) with Hausdorff dimension 1 such that, for any subset \(\varphi\neq B\subset A\), and any continuous map \(F: B\to \Sigma_N\), there is an increasing sequence \(\{ r(n) \}\) of positive integers such that \(\lim_{n\to \infty} \sigma^{r (n)}= F\) pointwise on \(B\); here \(\sigma^i\) denotes the \(i\)-th iterate of \(\sigma\).
scientific article; zbMATH DE number 786399