Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The classical KAM theorem for Hamiltonian systems via rational
  approximations   In this paper, we give a new proof of the classical KAM theorem on the
persistence of an invariant quasi-periodic torus, whose frequency vector
satisfies the Bruno-R\"ussmann condition, in real-analytic non-degenerate
Hamiltonian systems close to integrable. The proof, which uses rational
approximations instead of small divisors estimates, is an adaptation to the
Hamiltonian setting of the method we introduced in a previous work for
perturbations of constant vector fields on the torus.

36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an