Measurable Versions of Some Topological Properties for Diffeomorphisms with Continuous Foliations
Mathematical Problems in Engineering(2023)
Abstract
In this paper, the concepts of plaque expansivity, topological quasi-stability, and quasi-shadowing property for Borel measures are considered. It is proved that every plaque expansive measure with the quasi-shadowing property is topologically quasi-stable with respect to its continuous foliation. At the same time, some other properties of the topological quasi-stable measures, the plaque expansive measures, and measures with the quasi-shadowing on a compact Riemannian manifold are investigated.
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Key words
diffeomorphisms,topological properties,measurable versions
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