Mean chain transitivity and almost mean shadowing property of iterated function systems

Abstract

In this paper, we introduce the notions of mean chain transitivity, mean chain mixing, totally mean chain transitivity, and almost mean shadowing property to iterated function systems (IFS). We study the interrelations of these notions. We prove that an iterated function system is chain transitive if one of the constituent maps is surjective, and it has almost mean shadowing property.

Keywords

• transitivity
• shadowing
• pseudo-orbits
• chains
• iterated function systems