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http://dx.doi.org/10.22771/nfaa.2022.27.04.11

ERGODIC SHADOWING, $\underline{d}$-SHADOWING AND EVENTUAL SHADOWING IN TOPOLOGICAL SPACES  

Sonika, Akoijam (Department of Mathematics, Manipur University)
Khundrakpam Binod, Mangang (Department of Mathematics, Manipur University)
Publication Information
Nonlinear Functional Analysis and Applications / v.27, no.4, 2022 , pp. 839-853 More about this Journal
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.
Keywords
Hausdorff ergodic shadowing; Hausdorff $\underline{d}$-shadowing; Hausdorff eventual shadowing;
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