CAT（-1）度量空间中的拓扑混合
Topological mixing in CAT(-1) metric spaces
摘要：
若X是一个真CAT（-1）-空间，$Γ$是一个非初等离散等距群，它不连续地作用在X上，证明了商空间Y=X/ $Γ$上的测地流是拓扑混合的，条件是广义Busemann函数在边界$\partial X$上有零点，且测地线流的非徘徊集等于整个测地线商空间GY：=GX/ $Γ$（当Y是紧凑的时，后者是冗余的）。应用包括证明拓扑混合（A）紧负曲多面体，（B）紧测地线完备CAT（-1）-空间的等距群和（C）有限n维理想多面体。
英文摘要：
If X is a proper CAT(-1)-space and $Γ$ 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/$Γ$ is topologically mixing, provided that the generalized Busemann function has zeros on the boundary $\partial X$ and the non-wandering set of the flow equals the whole quotient space of geodesics GY:=GX/$Γ$ (the latter being redundant when Y is compact). Applications include the proof of topological mixing for (A) compact negatively curved polyhedra, (B) compact quotients of proper geodesically complete CAT(-1)-spaces by a one-ended group of isometries and (C) finite n-dimensional ideal polyhedra.
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