Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Minimal rates of entropy convergence for rank one systems

Pages: 773 - 796, Volume 6, Issue 4, October 2000      doi:10.3934/dcds.2000.6.773

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Frank Blume - Department of Mathematics, John Brown University, Siloam Springs, AR 72761, United States (email)

Abstract: 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, convergence rates, measure-preserving transformation, rank one.
Mathematics Subject Classification:  Primary: 28D05, 28D20.

Received: September 1997;      Revised: June 2000;      Available Online: August 2000.