English

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

Dynamical Systems 2026-01-07 v1

Abstract

For every flat surface, almost every flat surface in its SL(2,R)\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.

Keywords

Cite

@article{arxiv.2601.02979,
  title  = {Uniform distribution of saddle connection lengths in all $\mathsf{SL}(2,\mathbb{R})$ orbits},
  author = {Donald Robertson and Benjamin Dozier},
  journal= {arXiv preprint arXiv:2601.02979},
  year   = {2026}
}

Comments

23 pages, 2 figures