On Properties of Expansive Group Actions

Abstract

We study several properties of expansive group actions on metric spaces and obtain some relations between the expansivity for subgroup and group actions. Through counter examples, the necessity of hypothesis is justified. We also study the expansivity of covering maps. Further, we define orbit expansivity for group actions on topological spaces and use it to characterize expansive actions.

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Acknowledgements

Authors takes this opportunity to thank the referee(s) for his or her valuable comments.

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Correspondence to Ekta Shah.

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Barzanouni, A., Divandar, M.S. & Shah, E. On Properties of Expansive Group Actions. Acta Math Vietnam 44, 923–934 (2019). https://doi.org/10.1007/s40306-019-00330-9

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Keywords

  • Orbit expansive homeomorphism
  • Expansive group actions
  • Syndetic set
  • Subgroups

Mathematics Subject Classification (2010)

  • 37C85
  • 37C50
  • 37C75
  • 54H20