Minimal rates of entropy convergence for completely ergodic systems
Let \((X,{\mathcal B},m,T)\) be a completely ergodic measure-preserving dynamical system. It is shown that for some diverging positive sequence \(\{a_n:n\geq 1\}\) and some positive concave function \(g\) \(\liminf_{n \to\infty} H(\alpha_0^{n-1}) /a_n>0\) and \(\limsup_{n\to \infty}H (\alpha_0^{n-1})/g (\log_2n)>0\) for all nontrivial two set partitions of \(X\). This work continues the author investigations in [Ergodic Theory Dyn. Syst. 17, 45-70 (1997; Zbl 0891.28012)].
scientific article; zbMATH DE number 1270345