Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Through the Looking-Glass of the Grazing Bifurcation: Part I -
  Theoretical framework   It is well-known for vibro-impact systems that the existence of a periodic
solution with a low-velocity impact (so-called grazing) may yield complex
behavior of the solutions. In this paper we show that unstable periodic motions
which pass near the delimiter without touching it may give birth to chaotic
behavior of nearby solutions. We demonstrate that the number of impacts over a
period of forcing varies in a small neighborhood of such periodic motions. This
allows us to use the technique of symbolic dynamics. It is shown that chaos may
be observed in a two-sided neighborhood of grazing and this bifurcation
manifests at least two distinct ways to a complex behavior. In the second part
of the paper we study the robustness of this phenomenon. Particularly, we show
that the same effect can be observed in "soft" models of impacts.

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The categories of this paper are: cs
8
The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: physics
29
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: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc