Oscillating and nonsummable Radon-Nikodym cocycles along the forward geodesic of measure-class-preserving transformations
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910605060866048 |
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| author | Bell, Sasha Chu, Tasmin Rodgers, Owen |
| author_facet | Bell, Sasha Chu, Tasmin Rodgers, Owen |
| contents | We consider the least-deletion map on the Cantor space, namely the map that changes the first 1 in a binary sequence to 0, and construct product measures on $2^\mathbb{N}$ so that the corresponding Radon-Nikodym cocycles oscillate or converge to zero nonsummably along the forward geodesic of the map. These examples answer two questions of Tserunyan and Tucker-Drob. We analyze the oscillating example in terms of random walks on $\mathbb{Z}$, using the Chung-Fuchs theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16967 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Oscillating and nonsummable Radon-Nikodym cocycles along the forward geodesic of measure-class-preserving transformations Bell, Sasha Chu, Tasmin Rodgers, Owen Dynamical Systems Logic Primary 03E15, 37A40, Secondary 60G50, 37A20 We consider the least-deletion map on the Cantor space, namely the map that changes the first 1 in a binary sequence to 0, and construct product measures on $2^\mathbb{N}$ so that the corresponding Radon-Nikodym cocycles oscillate or converge to zero nonsummably along the forward geodesic of the map. These examples answer two questions of Tserunyan and Tucker-Drob. We analyze the oscillating example in terms of random walks on $\mathbb{Z}$, using the Chung-Fuchs theorem. |
| title | Oscillating and nonsummable Radon-Nikodym cocycles along the forward geodesic of measure-class-preserving transformations |
| topic | Dynamical Systems Logic Primary 03E15, 37A40, Secondary 60G50, 37A20 |
| url | https://arxiv.org/abs/2407.16967 |