Gromov-Hausdorff distances for dynamical systems

Nhan-Phu Chung

doi:10.3934/dcds.2020275

Article Contents

2020, Volume 40, Issue 11: 6179-6200. Doi: 10.3934/dcds.2020275

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Gromov-Hausdorff distances for dynamical systems

Nhan-Phu Chung

Department of Mathematics, Sungkyunkwan University, 2066 Seobu-ro, Jangan-gu, Suwon-si, Gyeonggi-do, 16419, Korea

Received: September 2019

Revised: May 2020

Published: July 2020

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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.

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Mathematics Subject Classification: 37C85, 37C40, 37C75.

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