Gromov-Hausdorff stability for group actions
type: Item
instance of: scholarly article
title: Gromov-Hausdorff stability for group actions
zbMATH Open document ID: 1466.37016
author: Meihua Dong
author: Keonhee Lee
author: C. A. Morales
published in: Discrete and Continuous Dynamical Systems
publication date: 2021-02-24T00:00:00Z
review text: The paper is a sequel to the work done by the first and third authors in [Discrete Contin. Dyn. Syst. 37, No. 7, 3531--3544 (2017; Zbl 1369.54024)] where a new notion of stability for homeomorphisms was introduced (Gromov-Hausdorff (GH) stability). Roughly speaking, this is a stability concept in a setting in which both the homeomorphism and the ambient space vary. Here the authors extend the notion of topological GH stability from homeomorphisms to finitely generated actions. The main result is that if an action is expansive and has the shadowing property, then it is topologically GH-stable. As a consequence they obtain examples of topologically GH-stable actions of the discrete Heisenberg group on tori. They also prove that the topological GH stability is an invariant under isometric conjugacy.
Mathematics Subject Classification ID: 37B25
Mathematics Subject Classification ID: 37B05
Mathematics Subject Classification ID: 37B65
Mathematics Subject Classification ID: 53C23
Mathematics Subject Classification ID: 22F10
zbMATH DE Number: 7314912
zbMATH Keywords: Gromov-Hausdorff compact metric space
zbMATH Keywords: group action
reviewed by: Athanase Papadopoulos
MaRDI profile type: Publication
full work available at URL: dcds.2020320
OpenAlex ID: W3080434740
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DOI: 10.3934/DCDS.2020320
description: scientific article; zbMATH DE number 7314912