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Effective counting on translation surfaces

Type of publication Peer-reviewed
Publikationsform Original article (peer-reviewed)
Author Nevo Amos, Rühr Rene, Weiss Barak,
Project Application of Homogeneous Dynamics: Effective Equidistribution and Counting
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Original article (peer-reviewed)

Journal Advances in Mathematics
Volume (Issue) 360
Page(s) 106890 - 106890
Title of proceedings Advances in Mathematics
DOI 10.1016/j.aim.2019.106890

Open Access

Type of Open Access Repository (Green Open Access)


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.