Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bridge to Hyperbolic Polygonal Billiards   It is well-known that billiards in polygons cannot be chaotic (hyperbolic).
Particularly Kolmogorov-Sinai entropy of any polygonal billiard is zero. We
consider physical polygonal billiards where a moving particle is a hard disc
rather than a point (mathematical) particle and show that typical physical
polygonal billiard is hyperbolic at least on a subset of positive measure and
therefore has a positive Kolmogorov- Sinai entropy for any positive radius of
the moving particle (provided that the particle is not so big that it cannot
move within a polygon). This happens because a typical physical polygonal
billiard is equivalent to a mathematical (point particle) semi-dispersing
billiard. We also conjecture that in fact typical physical billiard in polygon
is ergodic under the same conditions.

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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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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: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th