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TOPOLOGICAL ERGODIC SHADOWING AND TOPOLOGICAL PSEUDO-ORBITAL SPECIFICATION OF IFS ON UNIFORM SPACES
Thiyam Thadoi Devi,Khundrakpam Binod Mangang,Lalhmangaihzuala 경남대학교 기초과학연구소 2023 Nonlinear Functional Analysis and Applications Vol.28 No.4
In this paper, we discuss topological ergodic shadowing property and topological pseudo-orbital specification property of iterated function systems(\emph{IFS}) on uniform spaces. We show that an \emph{IFS} on a sequentially compact uniform space with topological ergodic shadowing property has topological shadowing property. We define the notion of topological pseudo-orbital specification property and investigate its relation to topological ergodic shadowing property. We find that a topologically mixing \emph{IFS} on a compact and sequentially compact uniform space with topological shadowing property has topological pseudo-orbital specification property and thus has topological ergodic shadowing property.