Local entropy theory for a countable discrete amenable group action
Local entropy theory for a countable discrete amenable group action
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DOI：
10.1016/j.jfa.2011.04.014
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发表时间：
2010-05
期刊：
影响因子：
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通讯作者：
Wen Huang;X. Ye;Guohua Zhang
中科院分区：
文献类型：
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作者：
Wen Huang;X. Ye;Guohua Zhang
研究了可数离散顺从群作用的熵的局部性质。对于这样的作用，建立了有限开覆盖的局部变分原理，由此导出了拓扑熵元组与测度熵元组之间的变分关系。在这样做的时候，它表明，两种测量理论熵的有限Borel覆盖相吻合。此外，还研究了两类特殊的作用量：具有一致正熵和完全正熵的系统。
The local properties of entropy for a countable discrete amenable group action are studied. For such an action, a local variational principle for a given finite open cover is established, from which the variational relation between the topological and measure-theoretic entropy tuples is deduced. While doing this it is shown that two kinds of measure-theoretic entropy for finite Borel covers coincide. Moreover, two special classes of such an action: systems with uniformly positive entropy and completely positive entropy are investigated.