On the dimension of stationary measures for random piecewise affine interval homeomorphisms
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866911869796614144 |
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| author | Barański, Krzysztof Śpiewak, Adam |
| author_facet | Barański, Krzysztof Śpiewak, Adam |
| contents | 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 $1$. In particular, we obtain singularity of these measures, answering partially a question of Alsedà and Misiurewicz from 2014. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2208_06394 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the dimension of stationary measures for random piecewise affine interval homeomorphisms Barański, Krzysztof Śpiewak, Adam Dynamical Systems 37E05, 37E10, 37H10, 37H15 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 $1$. In particular, we obtain singularity of these measures, answering partially a question of Alsedà and Misiurewicz from 2014. |
| title | On the dimension of stationary measures for random piecewise affine interval homeomorphisms |
| topic | Dynamical Systems 37E05, 37E10, 37H10, 37H15 |
| url | https://arxiv.org/abs/2208.06394 |