Tiling Billards on Triangle Tilings, and Interval Exchange Transformations
Autor: | Baird-Smith, Paul, Davis, Diana, Fromm, Elijah, Iyer, Sumun |
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Rok vydání: | 2018 |
Předmět: | |
Druh dokumentu: | Working Paper |
DOI: | 10.1112/jlms.12854 |
Popis: | 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. Comment: 31 pages, 19 figures, 2 appendices. Comments welcome! |
Databáze: | arXiv |
Externí odkaz: |
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