Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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ERGODIC SHADOWING, $\underline{d}$-SHADOWING AND EVENTUAL SHADOWING IN TOPOLOGICAL SPACES

  • Received : 2022.03.07
  • Accepted : 2022.04.07
  • Published : 2022.12.06
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Abstract

We define the notions of ergodic shadowing property, $\underline{d}$-shadowing property and eventual shadowing property in terms of the topology of the phase space. Secondly we define these notions in terms of the compatible uniformity of the phase space. When the phase space is a compact Hausdorff space, we establish the equivalence of the corresponding definitions of the topological approach and the uniformity approach. In case the phase space is a compact metric space, the notions of ergodic shadowing property, $\underline{d}$-shadowing property and eventual shadowing property defined in terms of topology and uniformity are equivalent to their respective standard definitions.

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Acknowledgement

We are thankful to the anonymous referees for their valuable comments and suggestions towards the improvement of the paper.

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