Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Averaging for Hamiltonian Systems with One Fast Phase and Small
  Amplitudes   The problem of averaging for systems with one fast phase was considered from
various points of view in many papers. The averaging method of Krylov and
Bogolyubov and methods of KAM theory originated this line of research, the most
complete results were obtained by Neishtadt, where the coefficients are assumed
real analytic. However, in many problems which are interesting from the point
of view of applications, analytic dependence ceases to hold in the
neighborhoods of some points. We show that one can choose a transformation such
that the averaging procedure of Neishtadt is applicable in these neighborhoods
and such passage to limit is uniform.

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The categories of this paper are: stat
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The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
1
The categories of this paper are: cs