Minimal rates of entropy convergence for completely ergodic systems期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Minimal rates of entropy convergence for completely ergodic systems

Authors:	Frank Blume

Affiliation:	(1) Department of Mathematics, John Brown University, 72761 Siloam Springs, AR, USA

Abstract:	If (X,T) is a completely ergodic system, then there exists a positive monotone increasing sequence {a _n} _n ^1/∞ with lim_n→∞a _n=∞ and a positive concave functiong defined on [1, ∞) for whichg(x)/x ² isnot integrable such that $mathop {lim inf }limits_{n to infty } Hleft( {alpha _0^{n - 1} } right)/a_n > 0 and mathop {lim inf }limits_{n to infty } Hleft( {alpha _0^{n - 1} } right)/gleft( {log _2 n} right) > 0$ for all nontrivial partitions α ofX into two sets.

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