Let X be a proper geodesic metric space which is -hyperbolic in the sense of Gromov. We study a class of functions on X, called horofunctions, which generalize Busemann functions. To each horofunction is associated a point in the boundary at infinity of X. Horofunctions are used to give a description of the boundary. In the case where X is the Cayley graph of a hyperbolic group À, we show, following ideas of Gromov sketched in his paper Hyperbolic groups, that the space of cocycles associated

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... horofunctions which take integral values on the vertices is a one-sided subshift of finite type.