Malaysian Journal of Mathematical Sciences, September 2022, Vol. 16, No. 3
On Topological Shadowing and Chain Properties of IFS on Uniform Spaces
Devi, T. T. and Mangang, K. B.
Corresponding Email: khubim@manipuruniv.ac.in
Received date: 10 June 2021
Accepted date: 14 July 2022
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.
Keywords: uniform space; shadowing; mixing; iterated function systems (IFS); transitivity
Indexing
