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arXiv · 1804.05920

GH-stability and Spectral Decomposition for Group Actions

Abdul Gaffar Khan·Pramod Das·Tarun Das
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Abstract

We study expansivity and the shadowing property for finitely generated group actions on metric spaces. We consider the projecting and lifting problems for actions having these properties. We prove that every expansive action with the shadowing property is strongly $GH$-stable (Gromov-Hausdorff stable). Finally, we introduce sequential shadowing property for finitely generated group actions on metric spaces and show that such shadowing is strong enough to imply the spectral decomposition property.

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Abdul Gaffar Khan, Pramod Das, Tarun Das. 2018-04-16. GH-stability and Spectral Decomposition for Group Actions. https://arxiv.org/abs/1804.05920

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