Abstract
Let (X,ϕ) be a compact metric flow without fixed points. We will be concerned with the entropy of flows which takes into consideration all possible reparametrizations of flows. In this paper, by establishing the Brin–Katok's entropy formula for flows without fixed points in the non-ergodic case, we prove the following result: for an ergodic ϕ-invariant measure μ,htopB(ϕ,Gμ(ϕ))=hμ(ϕ1), where Gμ(ϕ) is the set of generic points for μ and htopB(ϕ,Gμ(ϕ)) is the Bowen entropy on Gμ(ϕ). This extends the classical result of Bowen in 1973 to fixed-point free flows. Moreover, it is shown that the Bowen entropy can be determined via the local entropies of measures.
Published Version
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