Piecewise contractions defined by iterated function systems

Arnaldo Nogueira, Benito Pires, Rafael A. Rosales

Let ${\varphi }_1,\dots ,{\varphi }_n:[0,1]\to (0,1)$ be Lipschitz contractions. Let $I=[0,1)$, $x_0=0$ and $x_n=1$. We prove that for Lebesgue almost every $(x_1,...,x_{n-1})$ satisfying $0<x_1<\cd…