Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exceptional ergodic directions in Eaton lenses   We construct examples of ergodic vertical flows in periodic configurations of
Eaton lenses of fixed radius. We achieve this by studying a family of infinite
translation surfaces that are $\mathbb{Z}^2$-covers of slit tori. We show that
the Hausdorff dimension of lattices for which the vertical flow is ergodic is
bigger than 3/2. Moreover, the lattices are explicitly constructed.

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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph