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arXiv math/0410197math.GTmath.NT
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低高度测地线和马尔可夫谱

Low height geodesics and the Markoff spectrum

Thomas A. Schmidt, Mark Sheingorn

摘要:

我们分类,在最高弧的拓扑结构,低高度非简单测地线的模双曲穿孔球面上的三个椭圆不动点的二阶。在八种可能的类型中,恰好有一种是由测地线组成的,它们在尖点周围形成一个重子;我们用马尔可夫三元组来表示所有这样的测地线。我们还证明了连接两个椭圆不动点的任何测地线都有局部孤立高度。

英文摘要:

We classify, in terms of topology of highest arcs, low height non-simple geodesics on the modular hyperbolic punctured sphere with three elliptic fixed points of order two. Of eight possible types, exactly one consists of geodesics that form a bigon about the cusp; we express all such geodesics in terms of Markoff triples. We also show that any geodesic joining two elliptic fixed points has locally isolated height.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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