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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2107.02289 |
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Table of 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.