# American Institute of Mathematical Sciences

October  2000, 6(4): 773-796. doi: 10.3934/dcds.2000.6.773

## Minimal rates of entropy convergence for rank one systems

 1 Department of Mathematics, John Brown University, Siloam Springs, AR 72761, United States

Received  September 1997 Revised  June 2000 Published  August 2000

If $(X,T)$ is a rank one system and $g$ a positive concave funtion on $(0,\infty)$ such that $g(x)^2 / x^3$ is integrable, then limsup $_{n\to\infty}$ $H(\alpha_0^{n-1})$/$g(log_2 n) =\infty$, for all partitions $\alpha$ of $X$ into two sets with $\lim_{n\to\infty} \max\{\mu(A)|A\in\alpha_0^{n-1}\}=0$.
Citation: Frank Blume. Minimal rates of entropy convergence for rank one systems. Discrete & Continuous Dynamical Systems - A, 2000, 6 (4) : 773-796. doi: 10.3934/dcds.2000.6.773
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