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Tiling billards on triangle tilings, and interval exchange transformations.
- Source :
-
Journal of the London Mathematical Society . Jan2024, Vol. 109 Issue 1, p1-31. 31p. - Publication Year :
- 2024
-
Abstract
- 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 observe that, for a particular choice of triangle tiling, certain trajectories appear to approach the Rauzy fractal, under rescaling. [ABSTRACT FROM AUTHOR]
- Subjects :
- *REFRACTIVE index
*TILING (Mathematics)
*TRIANGLES
*POLYGONS
Subjects
Details
- Language :
- English
- ISSN :
- 00246107
- Volume :
- 109
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of the London Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 175054985
- Full Text :
- https://doi.org/10.1112/jlms.12854