Topological entropy of sets of generic points for actions of amenable groups

@article{Zheng2016TopologicalEO,
  title={Topological entropy of sets of generic points for actions of amenable groups},
  author={Dongmei Zheng and E. Chen},
  journal={Science China Mathematics},
  year={2016},
  volume={61},
  pages={869-880}
}
Let G be a countable discrete infinite amenable group which acts continuously on a compact metric space X and let μ be an ergodic G-invariant Borel probability measure on X. For a fixed tempered Følner sequence {Fn} in G with $${lim _{n \to + \infty }}\frac{{\left| {{F_n}} \right|}}{{\log n}} = \infty $$limn→+∞|Fn|logn=∞, we prove the following result: $$h_{top}^B\left( {{G_\mu },\left\{ {{F_n}} \right\}} \right) = {h_\mu }\left( {X,G} \right),$$htopB(Gμ,{Fn})=hμ(X,G), where Gμ is the set of… Expand
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