A class of continua that are not attractors of any IFS

TL;DR

This paper identifies conditions under which certain continua in Euclidean space cannot be attractors of any iterated function system, providing both theoretical criteria and a concrete example.

Contribution

It introduces a sufficient condition for continua not to be attractors of any IFS and constructs a specific example in the plane.

Findings

A continuum in R^n can be embedded so that it is not an IFS attractor.

Provided an example of a non-IFS attractor continuum in R^2.

Established a theoretical criterion for non-IFS attractors.

Abstract

This paper presents a sufficient condition for a continuum in $R^n$ to be embeddable in $R^n$ in such a way that its image is not an attractor of any iterated function system. An example of a continuum in $R^2$ that is not an attractor of any weakly contracting iterated function system is also given.