Dimension and measure theoretic entropy of a subshift in symbolic space
This short paper establishes a relationship between the Hausdorff dimension and the measure theoretic entropy of any subshift on the symbol space of \(N\) letters. The authors establish as well a variational principle for the Hausdorff dimension in terms of the measure theoretic entropy of ergodic invariant measures. In addition, the authors show that Bowen's formula for the Hausdorff dimension holds even when the assumption of Markov structure is eliminated.
scientific article; zbMATH DE number 1091413