Divergent on average directions of Teichmüller geodesic flow (Q2119382)

Understanding the recurrence and divergence properties of orbits of translation surfaces under the Teichmüller geodesic flow is a crucial tool for understanding the ergodic properties of directional flows on surfaces, a perspective going back to the foundational result of the second author [Trans. Am. Math. Soc. 324, No. 1, 235--254 (1991; Zbl 0733.32018)] showing that non-divergence of the Teichmüller orbit implies unique ergodicity of the vertical flow. Subsequently, \textit{S. Kerckhoff} et al. [Ann. Math. (2) 124, 293--311 (1986; Zbl 0637.58010)] showed that for a fixed surface, the set of directions with divergent trajectories has measure 0, and many subsequent papers have studied the Hausdorff dimension of the set of directions that behave unusually. The paper shows that the set of ``divergent on average'' trajectories has Hausdorff dimension exactly one-half, using a careful analysis of the possible sets of short saddle connections.