Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On ergodicity of foliations on $\mathbb{Z}^d$-covers of half-translation
  surfaces and some applications to periodic systems of Eaton lenses   We consider the geodesic flow defined by periodic Eaton lens patterns in the
plane and discover ergodic ones among those. The ergodicity result on Eaton
lenses is derived from a result for quadratic differentials on the plane that
are pull backs of quadratic differentials on tori. Ergodicity itself is
concluded for $\mathbb{Z}^d$-covers of quadratic differentials on compact
surfaces with vanishing Lyapunov exponents.

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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
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The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an