The growth rate of trajectories of a quadratic differential
The growth rate of trajectories of a quadratic differential
复制标题
二次微分轨迹的增长率
DOI：
10.1017/s0143385700005459
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发表时间：
1990
影响因子：
0.9
通讯作者：
H. Masur
中科院分区：
文献类型：
--
作者：
H. Masur
摘要 假设 q 是亏格 g ≥ 2 的紧黎曼曲面上的全纯二次微分。则 q 定义一个度量，除零点外均平坦。鞍形连接是连接两个零点且内部没有零点的测地线。本文证明了长度至多为T的鞍座数量的渐近增长率至多为T的二次方。并在台球中得到了应用。
Abstract Suppose q is a holomorphic quadratic differential on a compact Riemann surface of genus g ≥ 2. Then q defines a metric, flat except at the zeroes. A saddle connection is a geodesic joining two zeroes with no zeroes in its interior. This paper shows the asymptotic growth rate of the number of saddles of length at most T is at most quadratic in T. An application is given to billiards.