The Markov Spectra for Triangle Groups
The Markov Spectra for Triangle Groups
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三角形群的马尔可夫谱
DOI：
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发表时间：
1997
期刊：
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通讯作者：
L. Vulakh
中科院分区：
文献类型：
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作者：
L. Vulakh
本文应用双曲平面的Klein模型D_2，通过确定D_2中的测地线及其在射影平面上的极点，给出了一种确定Fuchsian群的Markov谱中的无限二叉树的方法。本文将这种方法应用于双曲平面上直角三角形各边反射所产生的群。给出了任意Hecke群的马氏谱的离散部分的完整描述。
Abstract Applying the Klein modelD2 of the hyperbolic plain and identifying the geodesics inD2 with their poles in the projective plane, the author has developed a method for determining infinite binary trees in the Markov spectrum for a Fuchsian group. In the present paper this method is applied to the groups generated by reflections in the sides of a rectangular triangle in the hyperbolic plane. The complete description of the discrete part of the Markov spectrum for any Hecke group is given.