Teichmueller曲线、三角形群和李雅普诺夫指数
Teichmueller curves, triangle groups, and Lyapunov exponents
摘要：
我们构造了一条由Fuchsian三角形群（m，n，\infty）均匀化的Teichmueller曲线，其中m<n.我们的建设包括Teichmueller曲线构造的Veech和沃德作为特殊情况。该构造本质上依赖于超几何微分算子的性质。对于较小的m，我们找到生成这些Teichmueller曲线的台球桌。我们将Kontsevich-Zorich上循环的某些所谓的李雅普诺夫指数表示为Teichmueller曲线上某些自然线丛的归一化度.我们确定的李雅普诺夫指数的Teichmueller曲线，我们构造。
英文摘要：
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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