Uniform distribution of saddle connection lengths in all $\mathsf{SL}(2,\mathbb{R})$ orbits

D. Robertson; Benjamin Dozier

doi:10.48550/arxiv.2601.02979

Uniform distribution of saddle connection lengths in all $\mathsf{SL}(2,\mathbb{R})$ orbits

arXiv (Cornell University) 2026 Preprint Open access

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Authors: D. Robertson, Benjamin Dozier

DOI: 10.48550/arxiv.2601.02979

Cited by: 0

Abstract

For every flat surface, almost every flat surface in its $\mathsf{SL}(2,\mathbb{R})$ orbit has the following property: the sequence of its saddle connection lengths in non-decreasing order is uniformly distributed in the unit interval.

Fields of Study & Subjects

Analytic and geometric function theory Mathematical Dynamics and Fractals Geometric and Algebraic Topology

Publication details

Journal / source: arXiv (Cornell University)
Publication date: 6 January 2026
Document type: Preprint