Abstract
In this work, we introduce a concept of expansiveness for actions of connected Lie groups. We study some of its properties and investigate some implications of expansiveness. We study the centralizer of expansive actions and introduce CW -expansiveness for pseudo-group actions. As an application, we prove positiveness of geometric entropy for expansive foliations and expansive group actions.
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Acknowledgements
The authors would like to thank professor Pablo Daniel Carrasco for his great help in the development of this work. His comments were essential to improve the content of this work. The authors also would like to thank the referees. Their valuable comments and suggestions were very useful and helped the authors to improve the exposition of this work.
Funding
A. A. was partially supported by CNPq, FAPERJ and PRONEX/DS from Brazil.
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Arbieto, A., Rego, E. Expansive Lie Group Actions. J Dyn Control Syst 29, 607–623 (2023). https://doi.org/10.1007/s10883-022-09600-6
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DOI: https://doi.org/10.1007/s10883-022-09600-6