F-expansivity for Borel measures

• Autor: Villavicencio Fernández H.
• Formato: artículo
• Fecha de Publicación: 2016
• Institución: Consejo Nacional de Ciencia Tecnología e Innovación
• Repositorio: CONCYTEC-Institucional
• Lenguaje: inglés
• OAI Identifier: oai:repositorio.concytec.gob.pe:20.500.12390/2791
• Enlace del recurso: https://hdl.handle.net/20.500.12390/2791; https://doi.org/10.1016/j.jde.2016.08.004
• Nivel de acceso: acceso abierto
• Materia: Support of a measure; Expansive flow; Expansive measure; Metric space; http://purl.org/pe-repo/ocde/ford#1.01.01

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.