Expansiveness of real flows
A flow F on X is called weakly expansive if F satisfies the property that for any \(\epsilon >0\) there exists \(\delta >0\) with the property that if there exist a pair of points x,y\(\in X\) and a strictly increasing surjective homeomorphism h: \(R\to R\) with \(h(0)=0\) such that \(d(f_ tx,f_{h(t)}y)<\delta\) for every \(t\in R\), then \(f_{h(t_ 0)}y\in f_{(t_ 0-\epsilon,t_ 0+\epsilon)}(\{x\})\) for some \(t_ 0\in R\). Theorem: A weakly expansive flow without fixed points must be an expansive flow.
scientific article; zbMATH DE number 4212997