Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

ON THE ALMOST SHADOWING PROPERTY FOR HOMEOMORPHISMS

  • 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)
  • Received : 2022.09.01
  • Accepted : 2022.11.02
  • Published : 2022.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we investigate some properties concerning the set of shadowable points for homeomorphisms. Then we show that the almost shadowing property is preserved by a topological conjugacy between homeomorphisms. Also, we give an example to illustrate our results.

Keywords

References

  1. N. Aoki and K. Hiraide, Topological Theory of Dynamical Systems, Elsevier Science B. V., 1994.
  2. J. Aponte and H. Villavicencio, Shadowable points for flows, J. Dyn. Control Syst., 24 (2018), no. 4, 701-719. https://doi.org/10.1007/s10883-017-9381-8
  3. A. Arbieto and E. Rego, Positive entropy through pointwise dynamics, Proc. Amer. Math. Soc., 148 (2020), 263-271. https://doi.org/10.1090/proc/14682
  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. N. Kawaguchi, Quantitative shadowable points, Dyn. Syst, 32 (2017), no. 4, 504-518. https://doi.org/10.1080/14689367.2017.1280664
  6. N. Koo, K. Lee and C. A. Morales, Pointwise topological stability, Proc. Edinb. Math. Soc., 61 (2018), no. 4, 1179-1191. https://doi.org/10.1017/S0013091518000263
  7. C. A. Morales, Shadowable points, Dyn Syst., 31 (2016), no. 3, 347-356. https://doi.org/10.1080/14689367.2015.1131813
  8. S. Y. Pilyugin, Shadowing in Dynamical Systems, Lect. Notes in Math., Springer-Verlag, Berlin, 1706 1999.
  9. P. Walters, On the pseudo-orbit tracing property and its relationship to stability, The Structure of Attractors in Dynamical Systems, Lecture Notes in Math., Springer-Verlag, Berlin, Heidelberg and New York, 668 1978, 231-244.