Chain Mixing and Chain Transitive Iterated Function Systems

Abstract

This paper considers some properties in topological dynamical systems in iterated function systems. First, we will introduce chain mixing and chain transitive iterated function systems then some results and an example is presented to compare with these notions in discrete dynamical systems. As our main result, using adding machine maps and topological conjugacy we show that chain mixing, chain transitive and chain recurrence properties in iterated function systems are equivalent.

AMS Classification:

• 37C50
• 37C15

Keywords:

• Adding machine maps
• Chain mixing
• Chain recurrent
• Chain transitive
• Iterated function sy.stems