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arXiv · 2209.11862

Pairs of saddle connections of typical flat surfaces on fixed affine orbifolds

Etienne Bonnafoux
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Abstract

We prove that the asymptotic number of pairs of saddle connections with length smaller than $L$ with bounded virtual area is quadratic for almost every translation surface with respect to any ergodic $SL(2,\mathbb{R})$-invariant measure. A key tool of the proof is that Siegel-Veech transforms of bounded functions with compact supports are in $L^{2+\kappa}$ for every $SL(2,\mathbb{R})$-invariant measure.

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Etienne Bonnafoux. 2022-09-23. Pairs of saddle connections of typical flat surfaces on fixed affine orbifolds. https://arxiv.org/abs/2209.11862

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