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

作　　者：Dongmei Zheng Ercai Chen 

机构地区：[1]School of Physical and Mathematical Sciences, Nanjing Tech University [2]School of Mathematical Sciences and Institute of Mathematics,Nanjing Normal University

出　　处：《Science China Mathematics》2018年第5期869-880,共12页中国科学：数学（英文版）

基　　金：supported by National Basic Research Program of China (Grant No. 2013CB834100);National Natural Science Foundation of China (Grant Nos. 11271191 and 11431012)

摘　　要：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 F?lner sequence {Fn} in G with limn→+∞|Fn|/log n= ∞, we prove the following result:h_top^B(G_μ, {F_n}) = h_μ(X, G),where G_μ is the set of generic points for μ with respect to {F_n} and h_top^B(G_μ, {F_n}) is the Bowen topological entropy(along {F_n}) on G_μ. This generalizes the classical result of Bowen(1973).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 F？lner sequence {Fn} in G with limn→＋∞｜Fn｜/log n= ∞, we prove the following result：h_top^B（G_μ, {F_n}） = h_μ（X, G）,where G_μ is the set of generic points for μ with respect to {F_n} and h_top^B（G_μ, {F_n}） is the Bowen topological entropy（along {F_n}） on G_μ. This generalizes the classical result of Bowen（1973）.

关 键 词：entropy generic point amenable group variational principle 

分 类 号：O189.11[理学—数学]