Effective counting on translation surfaces

2017/08/21 by Nevo, Amos, Rühr, Rene, Weiss, Barak
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1708.06263

Abstract

We prove an effective version of a celebrated result of Eskin and Masur: for any affine invariant manifold of translation surfaces, almost every translation surface has quadratic growth for the saddle connection holonomy vectors, with an effective bound of the error. We also provide effective versions of counting in sectors and in ellipses.

Related

• Counting pairs of saddle connections
• Counting saddle connections in a homology class modulo q
• Uniform Discreteness of the Holonomy vectors of translation surfaces
• Pairs of saddle connections of typical flat surfaces on fixed affine orbifolds
• Asymptotic counting of minimal surfaces in hyperbolic manifolds\n [according to Calegari, Marques and Neves]