动力系统的Gromov-Hausdorff距离
Gromov-Hausdorff distances for dynamical systems
摘要：
我们研究等变的Gromov-Hausdorff距离一般连续的行动，不一定是等距的，因为Zakiaya介绍。我们证明了如果一个作用是可扩张的，并且具有伪轨跟踪性质，那么它在我们的适应等变Gromov-Hausdorff拓扑下是稳定的。最后，利用Lott和Villani在研究曲率维数条件时的最优输运思想，研究了Wasserstein空间上局部紧顺从群作用的等变格罗莫夫-豪斯多夫收敛.
英文摘要：
We study equivariant Gromov-Hausdorff distances for general continuous actions which are not necessarily isometric as Fukaya introduced. We prove that if an action is expansive and has pseudo-orbit tracing property then it is stable under our adapted equivariant Gromov-Hausdorff topology. Finally, using Lott and Villani's ideas of optimal transport in studying curvature-dimension conditions, we investigate equivariant Gromov-Hausdorff convergence for actions of locally compact amenable groups on Wasserstein spaces.
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