Topological mixing in hyperbolic metric spaces

Details Topological mixing in hyperbolic metric spaces Topological mixing in hyperbolic metric spaces

1999-03-02

arxiv.org/abs/math/9903015v1

Mathematics

Geometric Topology

Scientific paper

If X is a hyperbolic metric space in the sense of Gromov and G a non- elementary discrete group of isometries acting properly discontinuously on X, it is shown that the geodesic flow on the quotient space Y=X/G is topologically mixing, provided that the non-wandering set of the flow equals the whole quotient space of geodesics GY:=GX/G and geodesics in X satisfy certain uniqueness and convergence properties. In addition, the boundary of X is assumed to be connected and a counter example is given concerning the necessity of this assumption.

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