On the hyperbolic limit points of groups acting on hyperbolic spaces |
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Authors: | Marco Pavone |
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Institution: | (1) Dipartimento di Matematica, Università di Palermo, Viale delle Scienze, I-90128 Palermo |
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Abstract: | We study the hyperbolic limit points of a groupG acting on a hyperbolic metric space, and consider the question of whether any attractive limit point corresponds to a unique
repulsive limit point. In the special case whereG is a (non-elementary) finitely generated hyperbolic group acting on its Cayley graph, the answer is affirmative, and the
resulting mapg
+↦g
−, is discontinuous everywhere on the hyperbolic boundary. We also provide a direct, combinatorial proof in the special case
whereG is a (non-abelian) free group of finite type, by characterizing algebraically the hyperbolic ends ofG.
Partially supported by a grant from M.U.R.S.T., Italy. |
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Keywords: | 1991 Mathematics Subject Classification" target="_blank">1991 Mathematics Subject Classification 20E08 51M10 20E05 |
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