COUNTING CLOSED GEODESICS IN MODULI SPACE

被引：30
作者：
Eskin, Alex [1 ]
Mirzakhani, Maryam [2 ]
机构：
[1] Univ Chicago, Dept Math, Chicago, IL 60637 USA
[2] Stanford Univ, Dept Math, Stanford, CA 94305 USA
来源：
JOURNAL OF MODERN DYNAMICS | 2011年 / 5卷 / 01期
基金：
美国国家科学基金会;
关键词：
Closed geodesics; Teichmuller space; Moduli space; TEICHMULLER FLOW; ASYMPTOTICS; GEOMETRY; DYNAMICS;
D O I：
10.3934/jmd.2011.5.71
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We compute the asymptotics, as R tends to infinity, of the number N(R) of closed geodesics of length at most R in the moduli space of compact Riemann surfaces of genus g. In fact, N(R) is the number of conjugacy classes of pseudo-Anosov elements of the mapping class group of a compact surface of genus g of translation length at most R.
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页码：71 / 105
页数：35
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