Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Resonant equilibrium configurations in quasi-periodic media: KAM theory   We develop an a-posteriori KAM theory for the equilibrium equations for
quasi-periodic solutions in a quasi-periodic Frenkel-Kontorova model when the
frequency of the solutions resonates with the frequencies of the substratum.
  The KAM theory we develop is very different both in the methods and in the
conclusions from the more customary KAM theory for Hamiltonian systems or from
the KAM theory in quasi-periodic media for solutions with frequencies which are
Diophantine with respect to the frequencies of the media. The main difficulty
is that we cannot use transformations (as in the Hamiltonian case) nor Ward
identities (as in the case of frequencies Diophantine with those of the media).
  The technique we use is to add an extra equation that ensures the
linearization of the equilibrium equation factorizes. To solve the extra
equation requires an extra counterterm. We compare this phenomenon with other
phenomena in KAM theory. It seems that this technique could be used in several
other problems.
  As a conclusion, we obtain that the perturbation expansions developed in the
previous paper \cite{SuZL15} converge when the potentials are in a codimension
one manifold in a space of potentials. The method of proof also leads to
efficient (low storage requirements and low operation count) algorithms to
compute the quasi-periodic solutions.

19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int