Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tiling Billards on Triangle Tilings, and Interval Exchange
  Transformations   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.

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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: physics