Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Partial hyperbolicity and foliations in $\mathbb{T}^3$   We prove that dynamical coherence is an open and closed property in the space
of partially hyperbolic diffeomorphisms of $\mathbb{T}^3$ isotopic to Anosov.
Moreover, we prove that strong partially hyperbolic diffeomorphisms of
$\mathbb{T}^3$ are either dynamically coherent or have an invariant
two-dimensional torus which is either contracting or repelling. We develop for
this end some general results on codimension one foliations which may be of
independent interest.

17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol