论文标题
在等级1 $ \ mathrm {sl} \ left（2，\ mathbb {r} \ right）$ - orbit关闭
Counting Closed Geodesics in Rank 1 $\mathrm{SL}\left(2,\mathbb{R}\right)$-orbit Closures
论文作者
论文摘要
我们获得三角形之间的相互作用数量的范围，因为表面的同伴结构沿Teichm {ü} ller geodesic在$ \ mathrm {Slrm {sl} \ left（2，\ mathbb {r} \ right）$ orbit在Modulian Space obelian Space obelian Space的等级1的范围。对于$ 0 \leqθ\ leq 1 $，我们在轨道闭合中的封闭地球封口数量上获得了一个指数限制，最多为$ r $，在带有短鞍连接的区域中至少花费其长度的$θ$折。
We obtain bounds on the numbers of intersections between triangulations as the conformal structure of a surface varies along a Teichm{ü}ller geodesic contained in an $\mathrm{SL}\left(2,\mathbb{R}\right)$-orbit closure of rank 1 in the moduli space of Abelian differentials. For $0 \leq θ\leq 1$, 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.
