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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.12120 |
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| _version_ | 1866910792268382208 |
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| author | Navas, Andrés |
| author_facet | Navas, Andrés |
| contents | We provide a large family of examples of affine isometries of the Banach spaces $C^0 (S^1)$, $L^1 (S^1)$ and $L^2 (S^1 \times S^1)$ that are fixed-point-free despite being recurrent (in particular, they have zero drift). These come from natural cocycles on the group of circle diffeomorphisms, namely the logarithmic, affine and (a variation of the) Schwarzian derivative. Quite interestingly, they arise from diffeomorphisms that are generic in an appropriate context. We also show how to promote these examples in order to obtain families of commuting isometries satisfying the same properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12120 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some examples of affine isometries of Banach spaces arising from 1-D dynamics Navas, Andrés Functional Analysis Dynamical Systems Group Theory 22F99, 37C20, 37E10, 46B04, 51F99 We provide a large family of examples of affine isometries of the Banach spaces $C^0 (S^1)$, $L^1 (S^1)$ and $L^2 (S^1 \times S^1)$ that are fixed-point-free despite being recurrent (in particular, they have zero drift). These come from natural cocycles on the group of circle diffeomorphisms, namely the logarithmic, affine and (a variation of the) Schwarzian derivative. Quite interestingly, they arise from diffeomorphisms that are generic in an appropriate context. We also show how to promote these examples in order to obtain families of commuting isometries satisfying the same properties. |
| title | Some examples of affine isometries of Banach spaces arising from 1-D dynamics |
| topic | Functional Analysis Dynamical Systems Group Theory 22F99, 37C20, 37E10, 46B04, 51F99 |
| url | https://arxiv.org/abs/2501.12120 |