Billingsley type theorem of Bowen polynomial entropy for fixed-point free flows

In this paper, we introduce the Bowen polynomial entropy and local polynomial entropy on subsets for flows which take into consideration all possible reparametrizations of flows. Through handling techniques for reparametrization balls, we show that the Bowen polynomial entropy can be determined by the local polynomial entropies of measures for fixed-point free flows, which extends Ma and Wen’s result.