Singular Stationary Measures for Random Piecewise Affine Interval Homeomorphisms

Krzysztof Barański; Adam Śpiewak

doi:10.1007/s10884-019-09807-5

Singular Stationary Measures for Random Piecewise Affine Interval Homeomorphisms

Krzysztof Barański, Adam Śpiewak

University of Warsaw

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We show that the stationary measure for some random systems of two piecewise affine homeomorphisms of the interval is singular, verifying partially a conjecture by Alsedà and Misiurewicz and contributing to a question by Navas on the absolute continuity of stationary measures, considered in the setup of semigroups of piecewise affine circle homeomorphisms. We focus on the case of resonant boundary derivatives.

Original language	English
Pages (from-to)	345-393
Number of pages	49
Journal	Journal of Dynamics and Differential Equations
Volume	33
Issue number	1
DOIs	https://doi.org/10.1007/s10884-019-09807-5
State	Published - Mar 2021
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2019, The Author(s).

Keywords

Minimal set
Random system
Semigroup of interval homeomorphisms
Stationary measure

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10.1007/s10884-019-09807-5

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abstract = "We show that the stationary measure for some random systems of two piecewise affine homeomorphisms of the interval is singular, verifying partially a conjecture by Alsed{\`a} and Misiurewicz and contributing to a question by Navas on the absolute continuity of stationary measures, considered in the setup of semigroups of piecewise affine circle homeomorphisms. We focus on the case of resonant boundary derivatives.",

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AB - We show that the stationary measure for some random systems of two piecewise affine homeomorphisms of the interval is singular, verifying partially a conjecture by Alsedà and Misiurewicz and contributing to a question by Navas on the absolute continuity of stationary measures, considered in the setup of semigroups of piecewise affine circle homeomorphisms. We focus on the case of resonant boundary derivatives.

KW - Minimal set

KW - Random system

KW - Semigroup of interval homeomorphisms

KW - Stationary measure

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Singular Stationary Measures for Random Piecewise Affine Interval Homeomorphisms

Abstract

Bibliographical note

Keywords

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