충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제34권1호
  • /
  • Pages.55-60
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  • 2021
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  • 1226-3524(pISSN)
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  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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ON PERIODIC SHADOWING OF INDUCED HYPERSPACE MAPS

  • Koo, Namjip (Department of Mathematics Chungnam National University) ;
  • Lee, Hyunhee (Department of Mathematics Chungnam National University) ;
  • Tsegmid, Nyamdavaa (Department of Mathematics Mongolian National University of Education)
  • 투고 : 2021.01.11
  • 심사 : 2021.01.22
  • 발행 : 2021.02.15
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초록

In this paper we deal with the preservation of the periodic shadowing property of induced hyperspatial systems. More precisely, we show that an expansive system has the periodic shadowing property if and only if its induced hyperspatial system has the periodic shadowing property.

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참고문헌

  1. J. Banks, Chaos for induced hyperspace maps, Chaos Solitons Fractals, 25 (2005), 681-685. https://doi.org/10.1016/j.chaos.2004.11.089
  2. W. Cordeiro, M. Denker, and X. Zhang, On specification and measure expansiveness, Discrete Contin. Dyn. Syst., 37 (2017), no. 4, 1941-1957. https://doi.org/10.3934/dcds.2017082
  3. A. Darabi and A.-M. Forouzanfar, Periodic shadowing and standard shadowing property, Asian-Eur. J. Math., 10 (2017), no. 1, 1750006, 9 pp. https://doi.org/10.1142/S1793557117500061
  4. L. Fernandez and C. Good, Shadowing for induced maps of hyperspaces, Fund. Math., 235 (2016), no. 3, 277-286. https://doi.org/10.4064/fm136-2-2016
  5. C. Good, J. Mitchell, and J. Thomas, Preservation of shadowing in discrete dynamical systems, J. Math. Anal. Appl., 485 (2020), 123767, in press. https://doi.org/10.1016/j.jmaa.2019.123767
  6. N. Koo and N. Tsegmid, On the density of various shadowing properties, Commun. Korean Math. Soc., 34 (2019), no. 3, 981-989. https://doi.org/10.4134/ckms.c180290
  7. P. Koscielniak, On genericity of shadowing and periodic shadowing property, J. Math. Anal. Appl., 310 (2005), no. 1, 188-196. https://doi.org/10.1016/j.jmaa.2005.01.053
  8. P. Ko'scielniak and M. Mazur, On C0 genericity of various shadowing properties, Discrete Contin. Dyn. Syst., 12 (2005), no. 3, 523-530. https://doi.org/10.3934/dcds.2005.12.523
  9. H. Lee, Stability of discrete dynamical systmes on hyperspaces, MSc thesis, Chungnam National University, 2019.
  10. H. Mendez, On density of periodic points for induced hyperspace maps, Topology Proc., 35 (2010), 281-290.
  11. N. Tsegmid, Periodic shadowing properties in dynamical systems, PhD thesis, Chungnam National University, 2019.
  12. W. R. Utz, Unstable homeomorphisms, Proc. Amer. Math. Soc., 1 (1950), 769-774. https://doi.org/10.1090/S0002-9939-1950-0038022-3