TOPOLOGICAL ERGODIC SHADOWING AND TOPOLOGICAL PSEUDO-ORBITAL SPECIFICATION OF IFS ON UNIFORM SPACES

Abstract

In this paper, we discuss topological ergodic shadowing property and topological pseudo-orbital specification property of iterated function systems(IFS) on uniform spaces.We show that an IFS on a sequentially compact uniform space with topological ergodics hadowing 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 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.