Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Energy separation in oscillatory Hamiltonian systems without any
  non-resonance condition   We consider multiscale Hamiltonian systems in which harmonic oscillators with
several high frequencies are coupled to a slow system. It is shown that the
oscillatory energy is nearly preserved over long times eps^{-N} for arbitrary
N>1, where eps^{-1} is the size of the smallest high frequency. The result is
uniform in the frequencies and does not require non-resonance conditions.

15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th