This is a note taken from V. Kaimanovich’s paper *Bowen-Margulis and Patterson measures on negatively curved compact manifolds*.

Let be a simply connected negatively curved manifold (the exponential map turns out to be a diffeomorphism for every by Cartan-Hadamard Theorem). Two geodesic rays on are called asymptotic if they they have a bounded distance in the future. Denote by the set of asymptotic classes of geodesic rays on . Then is called the visibility compactification of . Let .

Remark: Another view point is . Clearly it is independent of .

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