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On the hyperbolic orbital counting problem in conjugacy classes
- 作者：Jouni Parkkonen ; Frédéric Paulin
- 关键词：Counting ; Equidistribution ; Hyperbolic geometry ; Growth ; Conjugacy class ; 37C35 ; 20H10 ; 30F40 ; 53A35 ; 20G20
- 刊名：Mathematische Zeitschrift
- 出版年：2015
- 出版时间：April 2015
- 年：2015
- 卷：279
- 期：3-4
- 页码：1175-1196
- 全文大小：353 KB
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文摘
Given a discrete group \(\Gamma \) of isometries of a negatively curved manifold \({\widetilde{M}}\) , a non-trivial conjugacy class \({\mathfrak {K}}\) in \(\Gamma \) and \(x_0\in {\widetilde{M}}\) , we give asymptotic counting results, as \(t\rightarrow +\infty \) , on the number of orbit points \(\gamma x_0\) at distance at most \(t\) from \(x_0\) , when \(\gamma \) is restricted to be in \({\mathfrak {K}}\) , as well as related equidistribution results. These results generalise and extend work of Huber on cocompact hyperbolic lattices in dimension 2. We also study the growth of given conjugacy classes in finitely generated groups endowed with a word metric.
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