On the dimension of stationary measures for random piecewise affine interval homeomorphisms
Dynamical Systems
2024-05-08 v2
Abstract
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 . In particular, we obtain singularity of these measures, answering partially a question of Alsed\`a and Misiurewicz from 2014.
Keywords
Cite
@article{arxiv.2208.06394,
title = {On the dimension of stationary measures for random piecewise affine interval homeomorphisms},
author = {Krzysztof Barański and Adam Śpiewak},
journal= {arXiv preprint arXiv:2208.06394},
year = {2024}
}
Comments
Error in Lemma 4.1 corrected. Final authors version to appear in Ergodic Theory Dynam. Systems