Veech surfaces and their periodic points
نویسندگان
چکیده
منابع مشابه
Periodic Points on Veech Surfaces and the Mordell-weil Group over a Teichmüller Curve
Periodic points are points on Veech surfaces, whose orbit under the group of affine diffeomorphisms is finite. We characterise those points as being torsion points if the Veech surfaces is suitably mapped to its Jacobian or an appropriate factor thereof. For a primitive Veech surface in genus two we show that the only periodic points are the Weierstraß points and the singularities. Our main too...
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Veech’s original examples of translation surfaces Vq enjoying what McMullen has dubbed “optimal dynamics” arise from appropriately gluing sides of two copies of the regular qgon, with q ≥ 3 . We show that every Vq whose trace field is of degree greater than 2 has non-periodic directions of vanishing SAF-invariant. (Calta-Smillie have shown that under appropriate normalization, the set of slopes...
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2 We give a gentle introduction to the basics of Veech surfaces, with an emphasis on the Veech Dichotomy, followed by a sketch of the present state of the literature. These notes arose from lectures for a summer school held at the Institute de Mathématiques de Luminy in June 2003. We thank the participants, especially Jayadev Athreya who prepared an initial set of notes, and other speakers for ...
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We study the SL(2,R)–infimal lengths of simple closed curves on half-translation surfaces. Our main result is a characterization of Veech surfaces in terms of these lengths. We also revisit the “no small virtual triangles” theorem of Smillie and Weiss and establish the following dichotomy: the virtual triangle area spectrum of a half-translation surface either has a gap above zero or is dense i...
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An Abelian differential gives rise to a flat structure (translation surface) on the underlying Riemann surface. In some directions the directional flow on the flat surface may contain a periodic region that is made up of maximal cylinders filled by parallel geodesics of the same length. The growth rate of the number of such regions counted with weights, as a function of the length, is quadratic...
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ژورنال
عنوان ژورنال: Conformal Geometry and Dynamics of the American Mathematical Society
سال: 2016
ISSN: 1088-4173
DOI: 10.1090/ecgd/296