Tiling Billards on Triangle Tilings, and Interval Exchange Transformations

Autor: Baird-Smith, Paul, Davis, Diana, Fromm, Elijah, Iyer, Sumun
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
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