Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Upper bound on the number of collisions of pinned billiard balls   We consider systems of "pinned balls," i.e., balls that have fixed positions
and pseudo-velocities. Pseudo-velocities change according to the same rules as
those for velocities of totally elastic collisions between moving balls. The
times of possible pseudo-collisions for different pairs of pinned balls are
chosen in an exogenous way. We give an explicit upper bound for the maximum
number of pseudo-collisions for a system of $n$ pinned balls in a
$d$-dimensional space. The proof is based on analysis of foldings, i.e.,
mappings that formalize the idea of folding a piece of paper along a crease. We
prove an upper bound for the size of an orbit of a point subjected to foldings.

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The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
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The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th