We study equivariant Gromov-Hausdorff distances for general actions which are not necessarily isometric as Fukaya introduced. We prove that if an action is expansive and has the 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, we investigate equivariant Gromov-Hausdorff convergence for actions of locally compact amenable groups on Wasserstein spaces.

中文翻译：

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动力系统的Gromov-Hausdorff距离

我们研究一般动作的等距Gromov-Hausdorff距离，而不一定像Fukaya所介绍的那样是等距的。我们证明，如果一个动作是可扩展的并且具有伪轨道跟踪特性，那么它在我们适应的等变Gromov-Hausdorff拓扑下是稳定的。最后，使用Lott和Villani的最佳运输思想，我们研究了等变量Gromov-Hausdorff收敛性对Wasserstein空间上局部紧凑的可顺应群的作用。