Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A semi-classical K.A.M. theorem   We consider a semi-classical completely integrable system defined by a
$\hbar$-pseudodifferential operator $\hat{H}$ on the torus $\mathbb{T}^{d}$. In
order to study perturbed operators of the form $\hat{H}+\hbar^{\kappa}\hat{K}$,
where $\hat{K}$ is an arbitrary pseudodifferential operator and $\kappa>0$, we
prove the conjugacy to a suitable normal form. This is then used to construct a
large number of quasimodes.

17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas