Singular Stationary Measures for Random Piecewise Affine Interval Homeomorphisms
Singular Stationary Measures for Random Piecewise Affine Interval Homeomorphisms
We study stationary measures for iterated function systems (considered as random dynamical systems) consisting of two piecewise affine interval homeomorphisms, called Alsed\`a--Misiurewicz (AM) systems. We prove that for an open set of parameters, the unique non-atomic stationary measure for an AM-system has Hausdorff dimension strictly smaller than $1$. In particular, …