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Teichmüller curves, triangle groups, and Lyapunov exponents. (English) Zbl 1203.37049
The authors construct Teichmüller curves which are uniformised by some Fuchsian triangle group commensurable to $$\Delta(m,n,\infty)$$, for each $$m,n \leq \infty$$. Their construction includes the Teichmüller curves obtained by Veech and C. C. Ward as special cases. Their approach uses hypergeometric differential operators. For small values of $$m$$, they find billard tables which generate these Teichmüller curves. Finally, they determine the Lyapunov exponents for these Teichmüller curves.

##### MSC:
 37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) 14D07 Variation of Hodge structures (algebro-geometric aspects) 30F10 Compact Riemann surfaces and uniformization 30F60 Teichmüller theory for Riemann surfaces 37D50 Hyperbolic systems with singularities (billiards, etc.) (MSC2010) 20H10 Fuchsian groups and their generalizations (group-theoretic aspects)
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