Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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SHADOWABLE POINTS FOR FINITELY GENERATED GROUP ACTIONS

  • Kim, Sang Jin (Department of Mathematics Chungnam National University) ;
  • Lee, Keonhee (Department of Mathematics Chungnam University)
  • Received : 2018.10.01
  • Accepted : 2018.10.04
  • Published : 2018.11.15
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Abstract

In this paper we introduce the notion of shadowable points for finitely generated group actions on compact metric spaace and prove that the set of shadowable points is invariant and Borel set and if chain recurrent set contained shadowable point set then it coincide with nonwandering set. Moreover an action $T{\in}Act(G, X)$ has the shadowing property if and only if every point is shadowable.

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References

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