Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of non-sticking periodic oscillations obtained via the
  averaging method in discontinuous systems. I. Smooth outside of the
  discontinuity surfaces systems   In this paper the statement of the second Bogolyubov's theorem on periodic
solutions of smooth systems with small parameter is justified for
discountinuous systems. It is assumed that the generating solution intersects
the discontinuity hyperplanes transversally and that the system is smooth
outside of these hyperplanes. Such a situation is natural for mechanical
systems with dry friction and without constraints and sticking of oscillations.
To illustrate the result we prove stability of the velocity of
vibration-induced displacement.

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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin