Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fibered rotation vector and hypoellipticity for quasiperiodic cocycles
  in compact Lie groups   Using weak solutions to the conjugation equation, we define a fibered
rotation vector for almost reducible quasi-periodic cocycles in $\mathbb{T}^{d}
\times G$, $G$ a compact Lie group, over a Diophantine rotation. We then prove
that if this rotation vector is Diophantine with respect to the rotation in
$\mathbb{T}^{d}$, the cocycle is smoothly reducible, thus establishing a
hypoellipticity property in the spirit of the Greenfield-Wallach conjecture in
PDEs.

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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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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: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol