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arXiv · 2601.02979

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

Donald Robertson·Benjamin Dozier
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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.

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Donald Robertson, Benjamin Dozier. 2026-01-06. Uniform distribution of saddle connection lengths in all $\mathsf{SL}(2,\mathbb{R})$ orbits. https://doi.org/10.1007/s10711-023-00800-3

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