Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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TOPOLOGICAL STABILITY AND SHADOWING PROPERTY FOR GROUP ACTIONS ON METRIC SPACES

  • Yang, Yinong (School of Mathematical Sciences Beihang University)
  • Received : 2020.02.27
  • Accepted : 2020.05.14
  • Published : 2021.03.01
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Abstract

In this paper, we introduce the notions of expansiveness, shadowing property and topological stability for group actions on metric spaces and give a version of Walters's stability theorem for group actions on locally compact metric spaces. Moreover, we show that if G is a finitely generated virtually nilpotent group and there exists g ∈ G such that if Tg is expansive and has the shadowing property, then T is topologically stable.

Keywords

Acknowledgement

This work was financially supported by China Postdoctoral Science Foundation 2020M670082.

References

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