Skip to main content
SpringerLink
Log in

Several Dynamics of Dynamical Systems with the Eventual Shadowing Property

  • Published:
Acta Mathematica Sinica, English Series Aims and scope Submit manuscript

Abstract

In this article, we provide some sufficient conditions for the dynamical systems with the eventual shadowing property to have positive topological entropy and several equivalent conditions for the dynamical systems with the eventual shadowing property to be mixing.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Ahmadi, D. D., Hosseini, M.: Sub-shadowings. Nonlinear Anal., 72, 3759–3766 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Arbieto, A., Rego, E.: Positive entropy through pointwise dynamics. Proc. Amer. Math. Soc., 148(1), 262–271 (2020)

    MathSciNet  MATH  Google Scholar 

  3. Blank, M. L.: Deterministic properties of stochastically perturbed dynamical systems (in Russian). Teor. Veroyatnost. iPrimenen., 33(4), 659–671 (1988)

    MATH  Google Scholar 

  4. Blank, M. L.: Metric properties of e-trajectories of dynamical systems with stochastic behaviour. Ergodic Theory Dynam. Syst., 8, 365–378 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chen, Z. J., Li, J., Lü, J.: Point transitivity, Δ-transitivity and multi-minimality. Ergodic Theory Dyn. Syst., 35, 1423–1442 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  6. Dastjerdi, D. A., Hosseini, M.: Shadowing with chain transitivity. Topology Appl., 156, 2193–2195 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Dong, M., Jung, W. and Morales, C.: Eventually shadowable points. Qual. Theory Dyn. Syst., 19(1), Paper No. 16, 11 pp. (2020)

    Google Scholar 

  8. Good, C., Meddaugh, J: Orbital shadowing, internal chain transitivity and ω-limit sets. Ergodic Theory Dyn. Syst., 38(1), 143–154 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  9. Gu, R. B.: The asymptotic average shadowing property and transitivity. Nonlinear Anal., 67, 1680–1689 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  10. Kawaguchi, N.: Entropy points of continuous maps with the sensitivity and the shadowing property. Topology Appl., 210, 8–15 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  11. Kawaguchi, N.: Properties of shadowable points: chaos and equicontinuity. Bull. Braz. Math. Soc., 48(4), 599–622 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  12. Kawaguchi, N.: Quantitative shadowable points. Dyn. Syst., 32(4), 504–518 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  13. Kulczycki, M., Kwietniak, D., Oprocha, P.: On almost specification and average shadowing properties. Fund. Math., 224, 241–278 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  14. Kulczycki, M., Oprocha, P.: Exploring the asymptotic average shadowing property. J. Difference Equ. Appl., 16, 1131–1140 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  15. Kwietniak, D., Oprocha, P.: On weak mixing, minimality and weak disjoiness ofall iterates. Ergodic Theory Dyn. Syst., 32, 1661–1672 (2012)

    Article  MATH  Google Scholar 

  16. Li, J., Oprocha, P.: Shadowing property, weak mixing and regular recurrence. J. Dyn. Diff. Equ., 25(4), 1233–1249 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  17. Moothathu, T. K. S.: Diagonal points having dense orbit. Colloq. Math., 120, 127–138 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  18. Moothathu, T. K. S.: Implications of pseudo-orbit tracing property for continuous maps on compacta. Topology Appl., 158, 2232–2239 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  19. Morales, C. A.: Shadowable points. Dyn. Syst., 313(3), 347–356 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  20. Oprocha, P., Dastjerdi, D. A., Hosseini, M.: On partial shadowing of complete pseudo-orbits. J. Math. Anal. Appl., 402, 47–56 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  21. Shimomura, T.: Chain recurrence and P.O.T.P.. In: Dynamical Systems and Singular Phenomena. World. Sci. Adv. Ser. Dynam. Systems, 2, 224–241 (1986)

  22. Wang, H. Y., Fu, H. M., Diao, S. L.: Chain mixing, shadowing properties and multi-transitivity. Bull. Iranian Math. Soc., 45, 1605–1648 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  23. Wang, Q., Yang, R. S.: Pointwise pseudo-orbit tracing property and chaos. J. Math. Res. Expos., 28(2), 413–420 (2008)

    MathSciNet  MATH  Google Scholar 

  24. Wu, X. X., Oprocha, P., Chen, G. R.: On various definitions of shadowing with average error in tracing. Nonlinearity, 29, 1942–1972 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  25. Ye, X. D., Zhang, G. H.: Entropy points and applications. Trans. Amer. Math. Soc., 359, 6167–6186 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  26. Zhou, Z. L.: Weakly almost periodic point and measure centre. Sci. China Math., 36(2), 142–153 (1993)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Nanchang University, Nanchang, 330031, P. R. China

    Xue Rong Xie & Jian Dong Yin

Authors
  1. Xue Rong Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jian Dong Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jian Dong Yin.

Ethics declarations

The authors declare no conflict of interest.

Additional information

Supported by the National Natural Science Foundation of China (Grant No. 12061043)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xie, X.R., Yin, J.D. Several Dynamics of Dynamical Systems with the Eventual Shadowing Property. Acta. Math. Sin.-English Ser. 39, 1907–1918 (2023). https://doi.org/10.1007/s10114-023-1478-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-023-1478-2

Keywords

MR(2010) Subject Classification

Search

Navigation