Some examples of minimal Cantor set for IFSs with overlap

TL;DR

This paper presents specific examples of iterated function systems with overlapping intervals that generate minimal sets homeomorphic to the Cantor set, illustrating complex dynamics in such systems.

Contribution

It provides explicit examples of IFSs with overlap whose semigroup actions have minimal Cantor sets, advancing understanding of overlapping IFS dynamics.

Findings

Examples of IFSs with minimal Cantor sets are constructed.

Overlapping IFSs can produce complex minimal sets.

The semigroup actions in these systems are shown to have Cantor set minimal sets.

Abstract

We give some examples of IFSs with overlap on the interval such that the semigroup action they give rise to has a minimal set homeomorphic to the Cantor set.