Dynamical Systems and Numerical Analysis: the Study of Measures generated by Uncountable I.F.S

TL;DR

This paper investigates measures produced by uncountably infinite affine iterated function systems, providing numerical methods and rigorous results to determine their absolute or singular continuity properties.

Contribution

It introduces new numerical techniques and theoretical results for analyzing the measure properties of uncountable affine IFS.

Findings

Established criteria for measure absolute continuity.

Developed numerical algorithms for measure analysis.

Identified conditions leading to singular measures.

Abstract

Measures generated by Iterated Function Systems composed of uncountably many one--dimensional affine maps are studied. We present numerical techniques as well as rigorous results that establish whether these measures are absolutely or singular continuous.