On Topological Shadowing and Chain Properties of IFS on Uniform Spaces

Abstract

We define notions such as pseudo-orbit, topological shadowing, and topological chain transitivity of iterated function systems on compact uniform spaces. We prove that these notions are invariant under topological conjugacy on a compact uniform space. For an IFS on a compact uniform space with topological shadowing property, we show that the topological chain transitivity implies topological transitivity. We also show that in a connected compact uniform space, notions such as topological chain mixing, totally topological chain transitive, topological chain transitive, and topological chain recurrent are equivalent.