Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Residual periodicity on the Markoff surface   A case study of arithmetic dynamics over the rationals on the Markoff surface
is presented, in particular the local-global dynamical property of strong
residual periodicity. The dynamical system induced by the composition of any
two of the reflections from the three special points at infinity on the Markoff
surface is shown to be strongly residually periodic. This residual periodicity
is explained by the existence of periodic conic sections of the Markoff surface
with no rational points. It is also proven that cutting these conic sections
from the surface eliminates strong residual periodicity.

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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: bayes-an
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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: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th