Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximate Squaring   We study the ``approximate squaring'' map f(x) := x ceiling(x) and its
behavior when iterated. We conjecture that if f is repeatedly applied to a
rational number r = l/d > 1 then eventually an integer will be reached. We
prove this when d=2, and provide evidence that it is true in general by giving
an upper bound on the density of the ``exceptional set'' of numbers which fail
to reach an integer. We give similar results for a p-adic analogue of f, when
the exceptional set is nonempty, and for iterating the ``approximate
multiplication'' map f_r(x) := r ceiling(x) where r is a fixed rational number.

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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph