Equivalent Condition of the Measure Shadowing Property on Metric Spaces

Jie Miao and Yinong Yang ()
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Jie Miao: School of Mathematics and Statistics, Liaoning University, Shenyang 110036, China
Yinong Yang: School of Mathematics and Statistics, Liaoning University, Shenyang 110036, China

Mathematics, 2024, vol. 12, issue 6, 1-12

Abstract: The concept referred to as the measure shadowing property for a dynamical system on compact metric space has recently been introduced, acting as an extension of the classical shadowing property by using the property of the Borel measures on the phase space. In this paper, we extend the concept of the measure shadowing property of continuous flows from compact metric spaces to the general metric spaces and demonstrate the equivalence relation between the measure shadowing property and the shadowing property for flows on metric spaces via the shadowable points.

Keywords: metric spaces; Borel measures; measure shadowing property; shadowing property; shadowable points (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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