대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제62권1호
  • /
  • Pages.187-199
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  • 2025
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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TOTALLY ERGODIC SHADOWING PROPERTY ON NONCOMPACT METRIC SPACES

  • Namjip Koo (Department of Mathematics Chungnam National University) ;
  • Hyunhee Lee (Department of Mathematics Chungnam National University)
  • 투고 : 2024.02.24
  • 심사 : 2024.07.31
  • 발행 : 2025.01.31
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초록

In this paper, we study the ergodic shadowing property for dynamical systems on noncompact metric spaces. More precisely, under the condition of bi-uniform continuity of homeomorphisms on a metric space, we show that a homeomorphism on a metric space has the ergodic shadowing property if and only if it has the totally ergodic shadowing property. We also investigate some recurrences and dynamical properties of the ergodic shadowing property. Furthermore, we give some examples related to our results.

키워드

과제정보

The first author was supported by the National Research Foundations of Korea (NRF) grant funded by the Korea government (MSIT)(No. 2020R1F1A1A01068032). The second author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (RS-2023-00271567). The authors are grateful to the referees for the comments on the previous version of this paper.

참고문헌

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