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Equivalent Condition of the Measure Shadowing Property on Metric Spaces

Author

Listed:
  • Jie Miao

    (School of Mathematics and Statistics, Liaoning University, Shenyang 110036, China)

  • Yinong Yang

    (School of Mathematics and Statistics, Liaoning University, Shenyang 110036, China)

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.

Suggested Citation

  • Jie Miao & Yinong Yang, 2024. "Equivalent Condition of the Measure Shadowing Property on Metric Spaces," Mathematics, MDPI, vol. 12(6), pages 1-12, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:6:p:799-:d:1353842
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