대한수학회지 (Journal of the Korean Mathematical Society)

  • 제58권6호
  • /
  • Pages.1421-1431
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  • 2021
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  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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PRESERVATION OF EXPANSIVITY IN HYPERSPACE DYNAMICAL SYSTEMS

  • Koo, Namjip (Department of Mathematics Chungnam National University) ;
  • Lee, Hyunhee (Department of Mathematics Chungnam National University)
  • 투고 : 2021.01.19
  • 심사 : 2021.07.06
  • 발행 : 2021.11.01
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초록

In this paper we study the preservation of various notions of expansivity in discrete dynamical systems and the induced map for n-fold symmetric products and hyperspaces. Then we give a characterization of a compact metric space admitting hyper N-expansive homeomorphisms via the topological dimension. More precisely, we show that C0-generically, any homeomorphism on a compact manifold is not hyper N-expansive for any N ∈ ℕ. Also we give some examples to illustrate our results.

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과제정보

This work was supported by the National Research Foundations of Korea (NRF) grant funded by the Korea government (MSIT)(No. 2020R1F1A1A01068032). The authors are grateful to the referee for the comments on the previous version of this paper.

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