Local entropy theory for a countable discrete amenable group action |
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| Authors: | Wen Huang Xiangdong Ye |
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| Institution: | a Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences and Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China
b School of Mathematical Sciences and LMNS, Fudan University, Shanghai 200433, China |
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| Abstract: | 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. |
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| Keywords: | Entropy Amenable group Variational principle Entropy tuple |
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