Symbolic coding for the geodesic flow associated to a word hyperbolic group
Symbolic coding for the geodesic flow associated to a word hyperbolic group
复制标题
与词双曲群相关的测地线流的符号编码
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
A. Papadopoulos
中科院分区：
文献类型：
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作者：
M. Coornaert;A. Papadopoulos
设Γ是一个字双曲群M. Gromov构造了一个紧空间，它具有一个直到轨道等价定义的流，称为Γ的测地线流。在特殊情况下，其中Γ是负截面曲率黎曼流形的基本群，是配备通常测地线流的流形的单位切丛。本文对每一个双曲群Γ，构造了一个有限型子移位和一个从这个子移位的悬置到上的连续映射，这个连续映射一致有界于一，并且把悬置流的每一个轨道送到测地线流的一个轨道上.
Abstract. Let Γ be a word hyperbolic group M. Gromov has constructed a compact space equipped with a flow which is defined up to orbit-equivalence and which is called the geodesic flow of Γ. In the special case where Γ is the fundamental group of a Riemannian manifold of negative sectional curvature, is the unit tangent bundle of the manifold equipped with the usual geodesic flow. In this paper, we construct, for every hyperbolic group Γ, a subshift of finite type and a continuous map from the suspension of this subshift onto , which is uniformly bounded-to-one and which sends each orbit of the suspension flow onto an orbit of the geodesic flow.