Effective counting on translation surfaces
Dynamical Systems
2019-11-11 v3
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.
Cite
@article{arxiv.1708.06263,
title = {Effective counting on translation surfaces},
author = {Amos Nevo and Rene Rühr and Barak Weiss},
journal= {arXiv preprint arXiv:1708.06263},
year = {2019}
}
Comments
updated version, accepted for publication in Adv. Math