Measurable Versions of Some Topological Properties for Diffeomorphisms with Continuous Foliations

Lin Wang, Xinsheng Wang and Lei Wang

Mathematical Problems in Engineering, 2023, vol. 2023, 1-11

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.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:6050079

DOI: 10.1155/2023/6050079

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