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

2022/09/23 by Bonnafoux, Etienne
#28C10 #30F30 #32G15 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2209.11862

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,ℝ)-invariant measure. A key tool of the proof is that Siegel-Veech transforms of bounded functions with compact supports are in L^2+κ for every SL(2,ℝ)-invariant measure.

Related

• Counting pairs of saddle connections
• Siegel-Veech transforms are in L²
• Counting saddle connections in a homology class modulo q
• Large-genus asymptotics of saddle connection Siegel-Veech constants
• The distribution of gaps for saddle connection directions