The gap distribution of slopes on the golden L

TL;DR

This paper provides an explicit formula for the limiting distribution of gaps between slopes of saddle connections on the golden L and related surfaces, marking the first such computation for a non-torus cover flat surface.

Contribution

It introduces the first explicit computation of the gap distribution for slopes on a non-torus cover translation surface, specifically the golden L.

Findings

Explicit formula for gap distribution on the golden L

Extension to surfaces in the SL(2, R)-orbit of the golden L

First such distribution computed for a non-torus cover surface

Abstract

We give an explicit formula for the limiting gap distribution of slopes of saddle connections on the golden L, or any translation surface in its SL(2, R)-orbit, in particular the double pentagon. This is the first explicit computation of the distribution of gaps for a flat surface that is not a torus cover.