Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Teichmueller curves, triangle groups, and Lyapunov exponents   We construct a Teichmueller curve uniformized by the Fuchsian triangle group
(m,n,\infty) for every m<n. Our construction includes the Teichmueller curves
constructed by Veech and Ward as special cases. The construction essentially
relies on properties of hypergeometric differential operators. For small m, we
find Billiard tables that generate these Teichmueller curves.
  We interprete some of the so-called Lyapunov exponents of the
Kontsevich--Zorich cocycle as normalized degrees of some natural line bundles
on a Teichmueller curves. We determine the Lyapunov exponents for the
Teichmueller curves we construct.

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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th