当前位置: X-MOL 学术Geom. Dedicata. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Dynamics on the Morse boundary
Geometriae Dedicata ( IF 0.5 ) Pub Date : 2021-02-10 , DOI: 10.1007/s10711-021-00600-7
Qing Liu

Let X be a proper geodesic metric space and let G be a group of isometries of X which acts geometrically. Cordes constructed the Morse boundary of X which generalizes the contracting boundary for CAT(0) spaces and the visual boundary for hyperbolic spaces. We characterize Morse elements in G by their fixed points on the Morse boundary \(\partial _MX\). The dynamics on the Morse boundary is very similar to that of a \(\delta \)-hyperbolic space. In particular, we show that the action of G on \(\partial _MX\) is minimal if G is not virtually cyclic. We also get a uniform convergence result on the Morse boundary which gives us a weak north-south dynamics for a Morse isometry. This generalizes the work of Murray in the case of the contracting boundary of a CAT(0) space.



中文翻译:

莫尔斯边界上的动力学

X为适当的测地度量空间,令GX的一组等距几何形状。Cordes构建了X的Morse边界,该边界概括了CAT(0)空间的收缩边界和双曲空间的可视边界。我们通过在摩尔斯边界\(\ partial _MX \)上的固定点来表征G中的摩尔斯元素。Morse边界上的动力学与\(\ delta \)双曲空间的动力学非常相似。特别地,我们证明了如果GG\(\ partial _MX \)上的作用最小。实际上不是周期性的。我们还在莫尔斯(Morse)边界上获得了一致的收敛结果,这使我们对莫尔斯(Morse)等距具有弱的南北动力学。这概括了在CAT(0)空间的收缩边界的情况下Murray的工作。

更新日期:2021-02-10
down
wechat
bug