A ratio ergodic theorem via tiling and uniformly syndetic markers
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866915503425978368 |
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| author | Miller, Benjamin D. Tserunyan, Anush |
| author_facet | Miller, Benjamin D. Tserunyan, Anush |
| contents | We prove a purely Borel/measureless version of Dowker's ratio ergodic theorem, from which we derive a strengthening of Dowker's original theorem with a precise identification of the limit of local ergodic ratios. This is done by implementing the pointwise tiling idea of [Tse18] in the more complex setting of continuum-to-one Borel transformations. Along the way, we establish a vanishing markers lemma for these transformations, which generalizes its well-known counterpart for invertible transformations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_06463 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A ratio ergodic theorem via tiling and uniformly syndetic markers Miller, Benjamin D. Tserunyan, Anush Dynamical Systems Logic 03E15, 28A05, 37B05 We prove a purely Borel/measureless version of Dowker's ratio ergodic theorem, from which we derive a strengthening of Dowker's original theorem with a precise identification of the limit of local ergodic ratios. This is done by implementing the pointwise tiling idea of [Tse18] in the more complex setting of continuum-to-one Borel transformations. Along the way, we establish a vanishing markers lemma for these transformations, which generalizes its well-known counterpart for invertible transformations. |
| title | A ratio ergodic theorem via tiling and uniformly syndetic markers |
| topic | Dynamical Systems Logic 03E15, 28A05, 37B05 |
| url | https://arxiv.org/abs/2208.06463 |