Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Birkhoff sums as distributions I: Regularity   We study Birkhoff sums as distributions. We obtain regularity results on such
distributions for various dynamical systems with hyperbolicity, as hyperbolic
linear maps on the torus and piecewise expanding maps on the interval. We also
give some applications, as the study of advection in discrete dynamical
systems.

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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin