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In this chapter, we study the shadowing and topologically stable measures for a flow on a compact metric space X. In Sect. 8.1, we introduce a notion of a shadowing measure for a flow on X, which is applied to characterize the shadowing flows. In Sect. 8.2, we introduce a concept of a topologically stable measure for a flow on X. Moreover, we present a measurable version of Walters’ stability theorem for flows which says that any expansive measure with shadowing is topologically stable.

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Shadowing and Topological Stability for Flows

  • 章节

  • 发表日期：

    2026年

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  • Keonhee Lee,
  • Carlos Morales,
  • Ngocthach Nguyen

摘要

In this chapter, we study the shadowing and topologically stable measures for a flow on a compact metric space X. In Sect. 8.1, we introduce a notion of a shadowing measure for a flow on X, which is applied to characterize the shadowing flows. In Sect. 8.2, we introduce a concept of a topologically stable measure for a flow on X. Moreover, we present a measurable version of Walters’ stability theorem for flows which says that any expansive measure with shadowing is topologically stable.