Uniformity of geodesic flow in non-integrable 3-manifolds
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911818973184000 |
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| author | Beck, J. Chen, W. W. L. Yang, Y. |
| author_facet | Beck, J. Chen, W. W. L. Yang, Y. |
| contents | Almost nothing is known concerning the extension of $3$-dimensional Kronecker--Weyl equidistribution theorem on geodesic flow from the unit torus $[0,1)^3$ to non-integrable finite polycube translation $3$-manifolds.
In the special case when a finite polycube translation $3$-manifold is the cartesian product of a finite polysquare translation surface with the unit torus $[0,1)$, we have developed a splitting method with which we can make some progress. This is a somewhat restricted system, in the sense that one of the directions is integrable.
We then combine this with a split-covering argument to extend our results to some other finite polycube translation $3$-manifolds which satisfy a rather special condition and where none of the $3$ directions is integrable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19958 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniformity of geodesic flow in non-integrable 3-manifolds Beck, J. Chen, W. W. L. Yang, Y. Dynamical Systems Number Theory 37E35, 11K38 Almost nothing is known concerning the extension of $3$-dimensional Kronecker--Weyl equidistribution theorem on geodesic flow from the unit torus $[0,1)^3$ to non-integrable finite polycube translation $3$-manifolds. In the special case when a finite polycube translation $3$-manifold is the cartesian product of a finite polysquare translation surface with the unit torus $[0,1)$, we have developed a splitting method with which we can make some progress. This is a somewhat restricted system, in the sense that one of the directions is integrable. We then combine this with a split-covering argument to extend our results to some other finite polycube translation $3$-manifolds which satisfy a rather special condition and where none of the $3$ directions is integrable. |
| title | Uniformity of geodesic flow in non-integrable 3-manifolds |
| topic | Dynamical Systems Number Theory 37E35, 11K38 |
| url | https://arxiv.org/abs/2403.19958 |