Uniformity in cube-covering systems
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866911890249089024 |
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| author | Beck, J. Chen, W. W. L. |
| author_facet | Beck, J. Chen, W. W. L. |
| contents | We establish various analogs of the Kronecker-Weyl equidistribution theorem that can be considered higher-dimensional versions of results established in our earlier investigation of the discrete 2-circle problem studied in 1969 by Veech. Whereas the Veech problem can be viewed as one of geodesic flow on a 2-dimensional flat surface, here we study geodesic flow in higher-dimensional flat manifolds. This is more challenging, as the overwhelming majority of the available proof techniques for non-integrable flat systems are based on arguments in dimension 2. For higher dimensions, we need a new approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_02289 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Uniformity in cube-covering systems Beck, J. Chen, W. W. L. Dynamical Systems 11K38, 37E35 We establish various analogs of the Kronecker-Weyl equidistribution theorem that can be considered higher-dimensional versions of results established in our earlier investigation of the discrete 2-circle problem studied in 1969 by Veech. Whereas the Veech problem can be viewed as one of geodesic flow on a 2-dimensional flat surface, here we study geodesic flow in higher-dimensional flat manifolds. This is more challenging, as the overwhelming majority of the available proof techniques for non-integrable flat systems are based on arguments in dimension 2. For higher dimensions, we need a new approach. |
| title | Uniformity in cube-covering systems |
| topic | Dynamical Systems 11K38, 37E35 |
| url | https://arxiv.org/abs/2107.02289 |