On Non-Uniformly Discrete Orbits

2024/09/09 by Bashan, Sahar
#Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2409.05935

Abstract

We study the property of uniform discreteness within discrete orbits of non-uniform lattices in SL₂(ℝ), acting on ℝ² by linear transformations. We provide quantitative consequences of previous results by using Diophantine properties. We give a partial result toward a conjecture of Lelièvre regarding the set of long cylinder holonomy vectors of the "golden L" translation surface: for any ε>0, three points of this set can be found on a horizontal line within a distance of ε of each other.

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