8 citations · 23 across the 8 of their papers we have counts for
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Uniform distribution of saddle connection lengths in all orbits
Donald Robertson, Benjamin Dozier
For every flat surface, almost every flat surface in its orbit has the following property: the sequence of its saddle connection lengths in non-decreasi…
Measure bound for translation surfaces with short saddle connections
Benjamin Dozier
We prove that any ergodic -invariant probability measure on a stratum of translation surfaces satisfies strong regularity: the measure of the set of surfaces with two non-…
Equidistribution of saddle connections on translation surfaces
Benjamin Dozier
Fix a translation surface , and consider the measures on coming from averaging the uniform measures on all the saddle connections of length at most . Then as …
Convergence of Siegel-Veech constants
Benjamin Dozier
We show that for any weakly convergent sequence of ergodic -invariant probability measures on a stratum of unit-area translation surfaces, the corresponding Siege…