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Possible rates of entropy convergence

  • FRANK BLUME (a1)
  • Published online: 01 April 2001

We introduce entropy convergence rates as isomorphism invariants for measure-preserving systems and prove several general facts concerning these rates for aperiodic systems, completely ergodic systems and rank-one systems. We will for example show that for any completely ergodic system $(X,T)$ and any non-trivial partition $\alpha$ of $X$ into two sets we have $\limsup_{n\rightarrow\infty}H(\alpha_0^{n-1})/g(\log_2n)=\infty$, whenever $g$ is a positive increasing function on $(0,\infty)$ such that $g(x)/x^2$ is integrable.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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