On the fine structure of stationary measures in systems which contract-on-average

Matthew Nicol, Nikita Sidorov, David Broomhead

Suppose $\{f_1,...,f_m\}$ is a set of Lipschitz maps of ${\mathbb{R}}^d$. We form the iterated function system (IFS) by independently choosing the maps so that the map $f_i$ is chose…