On the dimension of stationary measures for random piecewise affine interval homeomorphisms

Krzysztof Barański, Adam Śpiewak

Research output: Contribution to journalArticlepeer-review


We study stationary measures for iterated function systems (considered as random dynamical systems) consisting of two piecewise affine interval homeomorphisms, called Alsedà-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 Alsedà and Misiurewicz [Random interval homeomorphisms. Publ. Mat. 58(suppl.) (2014), 15-36].

Original languageEnglish
Pages (from-to)1473-1488
Number of pages16
JournalErgodic Theory and Dynamical Systems
Issue number6
StatePublished - 4 Jun 2024

Bibliographical note

Publisher Copyright:
© The Author(s), 2023. Published by Cambridge University Press.


Krzysztof Barański was supported by the National Science Centre, Poland, grant no. 2018/31/B/ST1/02495. Adam Śpiewak acknowledges support from the Israel Science Foundation, grant 911/19. A part of this work was done when the second author was visiting the Budapest University of Technology and Economics. We thank Balázs Bárány, Károly Simon and R. Dániel Prokaj for useful discussions, and the staff of the Institute of Mathematics of the Budapest University of Technology and Economics for their hospitality.

FundersFunder number
Israel Science Foundation911/19
Narodowe Centrum Nauki2018/31/B/ST1/02495


    • interval homeomorphism
    • random system
    • stationary measure


    Dive into the research topics of 'On the dimension of stationary measures for random piecewise affine interval homeomorphisms'. Together they form a unique fingerprint.

    Cite this