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By Ursula Hamenst Ädt


Abstract. Let X be a proper CAT(0)-space with visual boundary ∂X. Let G be a non-elementary group of isometries of X with limit set Λ ⊂ ∂X. We survey properties of the action of G on Λ under the assumption that G contains a rank-one element. Among others, we show that there is a dense orbit for the action of G on the complement of the diagonal ∆ in Λ × Λ and that pairs of fixed points of rank-one elements are dense in Λ × Λ − ∆. 1

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