F-expansivity for Borel measures

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Villavicencio Fernández H.
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Academic Press Inc.
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We introduce the notion of F-expansive measure by making the dynamical ball in [4] to depend on a given subset F of the set of all the reparametrizations H. We prove that these measures satisfy some interesting properties resembling the expansive ones. These include the equivalence with expansivity when F=H, the vanishing along the orbits, the absence of singularities in the support, the F-expansivity with respect to time t-maps, the invariance under equivalence and the characterization for suspensions. We also analyze the support of the F-expansive measures and prove that there exists a dense subset of measures (in the set of F-expansive measures) all of them with a common support. Finally, we extend to flows the recent result for homeomorphisms in [11]. © 2016 Elsevier Inc.
Palabras clave
Support of a measure, Expansive flow, Expansive measure, Metric space