Gromov-Hausdorff distances for dynamical systems
Dynamical Systems
2020-05-12 v4
Abstract
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.
Cite
@article{arxiv.1901.07232,
title = {Gromov-Hausdorff distances for dynamical systems},
author = {Nhan-Phu Chung},
journal= {arXiv preprint arXiv:1901.07232},
year = {2020}
}
Comments
We provide examples to illustrate our main results. We change the statement of Corollary 1.4. We also correct typos