Generalized Staircases: Recurrence and Symmetry
Generalized Staircases: Recurrence and Symmetry
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广义阶梯：递归和对称
DOI：
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发表时间：
2009
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通讯作者：
B. Weiss
中科院分区：
文献类型：
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作者：
B. Weiss
我们研究无限平移表面，它是紧凑平移表面的 Z 覆盖。我们获得了确保此类表面具有第一类 Fuchsian 的 Veech 群的条件，并给出了其直线流重现的充分必要条件。扩展 Hubert 和 Schmithusen 的结果，我们提供了无限非算术晶格表面以及具有无限生成的 Veech 群的表面的示例。
We study infinite translation surfaces which are Z-covers of compact translation surfaces. We obtain conditions ensuring that such surfaces have Veech groups which are Fuchsian of the first kind and give a necessary and sufficient condition for recurrence of their straight-line flows. Extending results of Hubert and Schmithusen, we provide examples of infinite non-arithmetic lattice surfaces, as well as surfaces with infinitely generated Veech groups.