Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Integrability of codimension-one invariant subbundles of
  partially hyperbolic skew-products   We prove there is a class of maps
$\gamma:\mathbb{T}^{2n}\rightarrow\mathbb{S}^1$ such that a conservative
dynamically coherent partially hyperbolic skew-product on
$\mathbb{T}^{2n}\times\mathbb{S}^1$ with fixed hyperbolic dynamics on the base
and rotation by angle $\gamma$ acting on the fibers have integrable hyperbolic
structure which also implies in particular that they are not contact
diffeomorphisms. In dimension $3$, we prove the same result using a standard
technique in Contact Geometry, namely, that of \emph{characteristic
foliations}, which gives a simple proof of the result but with more tight
restrcitions to the map $\gamma$.

4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
16
The categories of this paper are: stat