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

Minimal rates of entropy convergence for rank one systems

Frank Blume 1,

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 $\lim_{n\to\infty} \max\{\mu(A)|A\in\alpha_0^{n-1}\}=0$.
Keywords: Entropy, measure-preserving transformation, convergence rates, rank one..
Mathematics Subject Classification: Primary: 28D05, 28D2.
Citation: Frank Blume. Minimal rates of entropy convergence for rank one systems. Discrete & Continuous Dynamical Systems, 2000, 6 (4) : 773-796. doi: 10.3934/dcds.2000.6.773
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