A framework for the study of the qualitative dynamics of general Iterated Function Systems

TL;DR

This paper introduces a new qualitative-dynamics framework for general Iterated Function Systems on locally compact spaces, using graph representations to distinguish recurrent and gradient-like behaviors.

Contribution

It extends existing semiflow frameworks to IFSs via binary relations, enabling a global qualitative dynamics analysis.

Findings

Graph representation separates recurrent and gradient-like behaviors.

Framework applies to general IFSs on locally compact spaces.

Extends previous semiflow-based approaches.

Abstract

We develop a qualitative-dynamics framework for general Iterated Function Systems (IFSs) on locally compact spaces. Our approach extends to IFSs a framework recently developed in the semiflows setting by James Yorke and the present author based on binary relations (streams) that encode which point can be regarded as "downstream" from which. This leads to a graph representation of the global qualitative dynamics that separates recurrent behavior from gradient-like behavior.