Tiling Billards on Triangle Tilings, and Interval Exchange Transformations
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866911780265000960 |
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| author | Baird-Smith, Paul Davis, Diana Fromm, Elijah Iyer, Sumun |
| author_facet | Baird-Smith, Paul Davis, Diana Fromm, Elijah Iyer, Sumun |
| contents | We consider the dynamics of light rays in triangle tilings where triangles are transparent and adjacent triangles have equal but opposite indices of refraction. We find that the behavior of a trajectory on a triangle tiling is described by an orientation-reversing three-interval exchange transformation on the circle, and that the behavior of all the trajectories on a given triangle tiling is described by a polygon exchange transformation. We show that, for a particular choice of triangle tiling, certain trajectories approach the Rauzy fractal, under rescaling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1809_07876 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Tiling Billards on Triangle Tilings, and Interval Exchange Transformations Baird-Smith, Paul Davis, Diana Fromm, Elijah Iyer, Sumun Dynamical Systems 37E10, 37E05, 37E35 We consider the dynamics of light rays in triangle tilings where triangles are transparent and adjacent triangles have equal but opposite indices of refraction. We find that the behavior of a trajectory on a triangle tiling is described by an orientation-reversing three-interval exchange transformation on the circle, and that the behavior of all the trajectories on a given triangle tiling is described by a polygon exchange transformation. We show that, for a particular choice of triangle tiling, certain trajectories approach the Rauzy fractal, under rescaling. |
| title | Tiling Billards on Triangle Tilings, and Interval Exchange Transformations |
| topic | Dynamical Systems 37E10, 37E05, 37E35 |
| url | https://arxiv.org/abs/1809.07876 |