Minimal rates of entropy convergence for rank one systems

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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

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

Received September 1997 Revised June 2000 Published August 2000

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

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