Zero-one law of Hausdorff dimensions of the recurrent sets

Dong Han Kim, Bing Li

Let $(\Sigma ,\sigma )$ be the one-sided shift space with $m$ symbols and $R_n(x)$ be the first return time of $x\in \Sigma$ to the $n$-th cylinder containing $x$. Denote $$E^φ_{α,β}=\left\{x\inΣ:…