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 and Continuous Dynamical Systems, 2000, 6 (4) : 773-796. doi: 10.3934/dcds.2000.6.773
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