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We obtain bounds on the numbers of intersections between triangulations asthe conformal structure of a surface varies along a Teichm{\"u}ller geodesiccontained in an $\mathrm{SL}\left(2,\mathbb{R}\right)$-orbit closure of rank 1in the moduli space of Abelian differentials. For $0 \leq \theta \leq 1$, weobtain an exponential bound on the number of closed geodesics in the orbitclosure, of length at most $R$, that spend at least $\theta$-fraction of theirlength in a region with short saddle connections.

Counting Closed Geodesics in Rank 1 $\mathrm{SL}\left(2,\mathbb{R}\right)$-orbit Closures