Rényi entropies of aperiodic dynamical systems

被引：0
作者：
Floris Takens
Evgeny Verbitskiy
机构：
[1] University of Groningen,Department of Mathematics
[2] Eurandom,undefined
来源：
Israel Journal of Mathematics | 2002年 / 127卷
关键词：
Invariant Measure; Generalize Entropy; Lebesgue Space; Bernoulli Shift; Finite Partition;
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摘要：
In this paper we continue the study of Rényi entropies of measure-preserving transformations started in [22]. We have established there that for ergodic transformations with positive entropy, the Rényi entropies of orderq, q ∈ ℝ, are equal to either plus infinity (q < 1), or to the measure-theoretic (Kolmogorov-Sinai) entropy (q ≥ 1). The answer for non-ergodic transformations is different: the Rényi entropies of orderq > 1 are equal to the essential infimum of the measure-theoretic entropies of measures forming the decomposition into ergodic components. Thus, it is possible that the Rényi entropies of orderq > 1 are strictly smaller than the measure-theoretic entropy, which is the average value of entropies of ergodic components.
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页码：279 / 302
页数：23
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