Mathematik in den Naturwissenschaften Leipzig Affine diffeomorphisms of translation surfaces : Periodic points , Fuchsian groups , and arithmeticity
Mathematik in den Naturwissenschaften Leipzig Affine diffeomorphisms of translation surfaces : Periodic points , Fuchsian groups , and arithmeticity
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发表时间：
2003
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通讯作者：
P. Hubert;Thomas A. Schmidt
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作者：
P. Hubert;Thomas A. Schmidt
我们研究了具有丰富仿射微分同胚群的平移曲面。我们引入了“预格子”平移面的概念。其中包括W.Veech研究的格子平移面。我们的结果刻画了预格点平移曲面之间的算术曲面在这个群的作用下周期点集的无穷大。我们证明了存在预格子但非格子平移面，否定地回答了Veech的一个问题。我们研究超椭圆平移曲面的周期点。特别地，我们给出了周期点集和魏尔斯特拉斯点集重合的平移曲面的显式例子。
We study translation surfaces with rich groups of affine diffeomorphisms. We introduce the notion of “prelattice” translation surfaces. They include the lattice translation surfaces studied by W. Veech. Our results characterize arithmetic surfaces among prelattice translation surfaces by the infinity of the set of periodic points under the action of this group. We show that there are prelattice but nonlattice translation surfaces, negatively answering a question of Veech. We study periodic points of hyperelliptic translation surfaces. In particular, we give explicit examples of translation surfaces whose sets of periodic points and Weierstrass points coincide.