A characterization of the standard Reeb flow

Among the topological conjugacy classes of the continuous flows $\{ϕ^t\}$ whose orbit foliations are the planar Reeb foliation, there is one class called the standard Reeb flow. We show that $\{ϕ^t\}$ is conjugate to the standard Reeb flow if and only if $\{ϕ^t\}$ is conjugate to $\{ϕ^{λt}\}$ for any $λ>0$.

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