Topological Entropy of Sets of Generic Points for Actions of Amenable Groups
نویسندگان
چکیده
Let G be a countable discrete 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} inG with lim n→+∞ |Fn| logn =∞, we prove the following variational principle: h(Gμ, {Fn}) = hμ(X,G), where Gμ is the set of generic points for μ with respect to {Fn} and h(Gμ, {Fn}) is the Bowen topological entropy (along {Fn}) on Gμ. This generalizes the classical result of Bowen in 1973.
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