Shrinking rates of horizontal gaps for generic translation surfaces (Q6623102)

The main results here give precise decay rates for the difference in angle between a pair of almost horizontal saddle connections (geodesics starting and ending at singular points) on a translation surface. The proofs exploit the connection between the geometry of a translation surface and its orbit under the Teichmüller geodesic flow and then reduces the problem to a shrinking target problem for this flow. A key part of the toolboox available in this setting is exponential mixing for the flow and the estimates it provides, but for some of the settings needed here this is insufficient and different ideas are needed.