Applications of the Tarski-Kantorovitch Fixed-Point Principle to the study of Infinite Iterated Function Systems

TL;DR

This paper applies the Tarski-Kantorovitch fixed-point principle to analyze Infinite Iterated Function Systems, introducing new classes and studying properties of their canonical projections to understand their attractors.

Contribution

It introduces two new classes of Infinite Iterated Function Systems suitable for fixed-point analysis and investigates properties of their canonical projections.

Findings

Established results on fixed points for new IIFS classes

Analyzed properties of canonical projections

Connected fixed-point principles to IIFS attractors

Abstract

The aim of this paper is to establish some results regarding Infinite Iterated Function Systems with the help of the Tarski-Kantorovitch fixed-point principles for maps on partially ordered sets. To this end we introduce two new classes of Infinite Iterated Function Systems which are well suited for applying the aforementioned principle. We also study some properties of the canonical projection from the shift space of an Infinite Iterated Function System belonging to one of the two introduced classes to its attractor.