Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An `almost all versus no' dichotomy in homogeneous dynamics and
  Diophantine approximation   Let $Y_0$ be a not very well approximable $m\times n$ matrix, and let $M$ be
a connected analytic submanifold in the space of $m\times n$ matrices
containing $Y_0$. Then almost all $Y\in M$ are not very well approximable. This
and other similar statements are cast in terms of properties of certain orbits
on homogeneous spaces and deduced from quantitative nondivergence estimates for
`quasi-polynomial' flows on on the space of lattices.

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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: cs
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The categories of this paper are: comp-gas
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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: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin