论文标题
固定仿射轨道上典型平面表面的鞍座连接
Pairs of saddle connections of typical flat surfaces on fixed affine orbifolds
论文作者
论文摘要
我们证明，与任何Ergodic $ SL（2，\ Mathbb {r}）$ - 不变的度量相对于几乎每个翻译表面的渐近鞍座连接对的马鞍连接对的长度小于$ l $都是二次的。证明的一个关键工具是，带有紧凑型支持的有限函数的siegel-veech转换为$ l^{2+κ} $，对于每个$ sl（2，\ mathbb {r}）$ - 不变性措施。
We prove that the asymptotic number of pairs of saddle connections with length smaller than $L$ with bounded virtual area is quadratic for almost every translation surface with respect to any ergodic $SL(2,\mathbb{R})$-invariant measure. A key tool of the proof is that Siegel-Veech transforms of bounded functions with compact supports are in $L^{2+κ}$ for every $SL(2,\mathbb{R})$-invariant measure.
