Gaps of saddle connection directions for some branched covers of tori

Autor:	Sanchez, Anthony
Rok vydání:	2020
Předmět:	Mathematics - Dynamical Systems Mathematics - Geometric Topology 37A17 (Primary) 37D40 32G15 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We compute the gap distribution of directions of saddle connections for two classes of translation surfaces. One class will be the translation surfaces arising from gluing two identical tori along a slit. These yield the first explicit computations of gap distributions for non-lattice translation surfaces. We show that this distribution has support at 0 and quadratic tail decay. We also construct examples of translation surfaces in any genus $d>1$ that have the same gap distribution as the gap distribution of two identical tori glued along a slit. The second class we consider are twice-marked tori and saddle connections between distinct marked points. These results can be interpreted as the gap distribution of slopes of affine lattices. We obtain our results by translating the question of gap distributions to a dynamical question of return times to a transversal under the horocycle flow on an appropriate moduli space. Comment: 56 pages, 7 figures, made some contributions clearer such as the results on the transversal and affine lattices
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2004.04182 Zobrazit plný text záznamu View this record from Arxiv