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.
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Received: 25 January 2002 / Revised version: 20 August 2002
Mathematics Subject Classification (2000): 20F67, 20F65, 20F69, 53C23, 53C21, 37D40, 37B10, 54H20
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Coornaert, M., Papadopoulos, A. Symbolic coding for the geodesic flow associated to a word hyperbolic group. Manuscripta Math. 109, 465–492 (2002). https://doi.org/10.1007/s00229-002-0321-9
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DOI: https://doi.org/10.1007/s00229-002-0321-9