Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reducibility of first order linear operators on tori via Moser's theorem   In this paper we prove reducibility of classes of linear first order
operators on tori by applying a generalization of Moser's theorem on
straightening of vector fields on a torus. We consider vector fields which are
a $C^\infty$ perturbations of a constant vector field, and prove that they are
conjugated --by a $C^\infty$ torus diffeomorphism-- to a constant diophantine
flow, provided that the perturbation is small in some given $H^{s_1}$ norm and
that the initial frequency is in some Cantor-like set. Actually in the
classical results of this type the regularity of the change of coordinates
which straightens the perturbed vector field coincides with the class of
regularity in which the perturbation is required to be small. This improvement
is achieved thanks to ideas and techniques coming from the Nash-Moser theory.

4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex