Counting Closed Geodesics in Rank 1 SL(2,ℝ)-orbit Closures

2022/06/30 by Rached, John
#Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2207.00073

Abstract

We obtain bounds on the numbers of intersections between triangulations as the conformal structure of a surface varies along a Teichmüller geodesic contained in an SL(2,ℝ)-orbit closure of rank 1 in the moduli space of Abelian differentials. For 0 ≤ θ≤ 1, we obtain an exponential bound on the number of closed geodesics in the orbit closure, of length at most R, that spend at least θ-fraction of their length in a region with short saddle connections.

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