Dimension estimates for invariant measures of contracting-on-average iterated function systems

TL;DR

This paper provides bounds on the dimension of invariant measures for contracting-on-average iterated function systems in Euclidean space, enhancing understanding of their geometric properties.

Contribution

It introduces new methods to estimate the dimension of invariant measures for contracting-on-average systems, offering both upper and lower bounds.

Findings

Established upper and lower bounds for the dimension

Applied to systems in ^d space

Improved understanding of invariant measure geometry

Abstract

We estimate from above and below the dimension of invariant measure for contracting-on-average iterated function systems in $\R^d$.