On Equicontinuity, Transitivity and Distality of Iterated Function Systems

Abstract

In this paper, equicontinuity, transitivity, minimality, sensitivity, and distality of iterated function systems(IFS) have been discussed. The equicontinuity, almost equicontinuity, and distality of an IFS have been defined and some relevant results have been introduced and proved. The transitivity, minimality, and sensitivity of an IFS F have been investigated when each of the constituent maps f_λ has these properties and vice versa. It has been found that the IFS has these properties if at least one of the constituent maps f_λ has these properties but the converse statements are not true. We give counterexamples to support that the converse statements are not true. It has also been shown that an IFS F is distal if and only if the constituent maps f_λ are distal.

AMS Classification:

• 54H20
• 37B05
• 26A18

Keywords:

• Distality
• Equicontinuity
• Iterated function systems
• Sensitivity
• Transitivity