Gromov's boundary at infinity, drop the hypothesis on hyperbolicity It's an easy result that if we have two quasi isometric hyperbolic spaces, then their Gromov boundaries at infinity are homeomorphic.
I found online these notes where at page 8, prop 2.20 they seem to drop the hypothesis on hyperbolicity. They give two references (french articles) for the proof but I didn't found anything.
Hence, can someone give me a reference/proof/counterexample to the following statement?

Let X,Y proper geodesic spaces, and let $f\colon X \to Y$ be a quasi isometry between them, then $\partial_pX \cong \partial_{f(p)}Y$


Counter-examples are due to Buyalo in his paper "Geodesics in Hadamard spaces" and to Croke and Kleiner in an unpublished preprint. See also the later paper of Croke and Kleiner entitled "Spaces with nonpositive curvature and their ideal boundaries" which cites their preprint and gives further information.
