Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gauss map and Lyapunov exponents of interacting particles in a billiard   We show that the Lyapunov exponent (LE) of periodic orbits with Lebesgue
measure zero from the Gauss map can be used to determine the main qualitative
behavior of the LE of a Hamiltonian system. The Hamiltonian system is a
one-dimensional box with two particles interacting via a Yukawa potential and
does not possess Kolmogorov-Arnold-Moser (KAM) curves. In our case the Gauss
map is applied to the mass ratio $\gamma = m_2/m_1$ between particles. Besides
the main qualitative behavior, some unexpected peaks in the $\gamma$ dependence
of the mean LE and the appearance of 'stickness' in phase space can also be
understand via LE from the Gauss map. This shows a nice example of the relation
between the "instability" of the continued fraction representation of a number
with the stability of non-periodic curves (no KAM curves) from the physical
model. Our results also confirm the intuition that pseudo-integrable systems
with more complicated invariant surfaces of the flow (higher genus) should be
more unstable under perturbation.

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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: math