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Measurable Versions of Some Topological Properties for Diffeomorphisms with Continuous Foliations

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… Click to show full 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.

Keywords: quasi shadowing; diffeomorphisms continuous; measurable versions; topological properties; versions topological; properties diffeomorphisms

Journal Title: Mathematical Problems in Engineering
Year Published: 2023

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