Counting One-Sided Simple Closed Geodesics on Fuchsian Thrice Punctured Projective Planes
Counting One-Sided Simple Closed Geodesics on Fuchsian Thrice Punctured Projective Planes
复制标题
计算 Fuchsian 三次穿刺射影平面上的单边简单闭测地线
DOI：
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发表时间：
2017
影响因子：
1
通讯作者：
Michael Magee
中科院分区：
文献类型：
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作者：
Michael Magee
本文证明了在任意Fuchsian真实的射影平面上，当去掉三点时，长度为L的单边简单闭曲线的个数存在一个真实的渐近公式.增长指数与双曲度量无关，并且是非整数的，与Mirzakhani对可定向Fuchsian曲面上简单闭曲线的计数结果相反。
We prove that there is a true asymptotic formula for the number of one-sided simple closed curves of length $leq L$ on any Fuchsian real projective plane with three points removed. The exponent of growth is independent of the hyperbolic metric, and it is noninteger, in contrast to counting results of Mirzakhani for simple closed curves on orientable Fuchsian surfaces.