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Zbl 1106.37018
Gutkin, Eugene; Hubert, Pascal; Schmidt, Thomas A.
Affine diffeomorphisms of translation surfaces: periodic points, Fuchsian groups, and arithmeticity. (English)
[J] Ann. Sci. Éc. Norm. Supér. (4) 36, No. 6, 847-866 (2003). ISSN 0012-9593

Summary: We study translation surfaces with rich groups of affine diffeomorphisms -- "prelattice" surfaces. These include the lattice translation surfaces studied by W. Veech. We show that there exist prelattice but nonlattice translation surfaces. We characterize arithmetic surfaces among prelattice surfaces by the infinite cardinality of their set of points periodic under affine diffeomorphisms. We give examples of translation surfaces whose periodic points and Weierstrass points coincide.

MSC 2000:: *37C85 Dynamics of group actions other than $\bbfZ$ and $\bbfR$, etc.
20H10 Fuchsian groups and their generalizations (group theory)
30F35 Fuchsian groups and automorphic functions
37E99 Low-dimensional dynamical systems

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