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A Remark on Sensitivity and Li–Yorke Sensitivity of Iterated Function Systems

  • Ma, Cuina [1] ; Zhu, Peiyong [1]
    1. [1] University of Electronic Science and Technology of China

      University of Electronic Science and Technology of China

      China

  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 18, Nº 1, 2019, págs. 1-9
  • Idioma: inglés
  • DOI: 10.1007/s12346-018-0270-7
  • Enlaces
  • Resumen
    • This considers how sensitivity and Li–Yorke sensitivity on iterated function systems carry over to their products and proves that the sensitivity and Li–Yorke sensitivity are both preserved under iterations.

  • Referencias bibliográficas
    • 1. Akin, E., Kolyada, S.: Li–Yorke sensitivity. Nonlinearity 16(4), 1421–1433 (2003)
    • 2. Auslander, J., Yorke, J.A.: Interval maps, factors of maps, and chaos. Tohoku Math. J. First 32(2), 177–188 (1980)
    • 3. Bahabadi, Z.A.: Shadowing and average shadowing properties for iterated function systems. Georg. Math. J. 22(2), 179–184 (2016)
    • 4. Barnsley, M.F.: Fractals Everywhere. Academic Press Professional, London (1993)
    • 5. De ˇgirmenci, N., Koˇcak, ¸Sahin: Chaos in product maps. Turk. J. Math. 34(4), 593–600 (2010)
    • 6. Devaney, R.L.: An Introduction to Chaotic Dynamical Systems. Addison-Wesley, Reading (1989)
    • 7. Eirola, T., Nevanlinna, O., Pilyugin, S.Y.: Limit shadowing property. Numer. Funct. Anal. Optim. 18(1–2), 75–92 (1997)
    • 8. Elton, J.H., Piccioni, M.: Iterated function systems a rising from recursive estimation problems. Probab. Theory Relat. Fields 91(1), 103–114...
    • 9. Forte, B., Vrscay, E.R.: Solving the inverse problem for function/image approximation using iterated function systems. Fractals Complex...
    • 10. Ghane, F.H., Rezaali, E., Saleh, M., Sarizadeh, A.: Sensitivity of iterated function systems (2016). arXiv:1603.08243
    • 11. Li, J., Oprocha, P., Wu, X.: Furstenberg families, sensitivity and the space of probability measures. Nonlinearity 30, 987–1005 (2017)
    • 12. Hutchinson, J.E.: Fractals and self-similarity. Indiana Univ. Math. J. 30(5), 713–747 (1981)
    • 13. Li, R., Zhou, X.: A note on chaos in product maps. Turk. J. Math. 37(4), 665–675 (2013)
    • 14. Montrucchio, L., Privileggi, F.: Fractal steady states instochastic optimal control models. Ann. Oper. Res. 88, 183–197 (1999)
    • 15. Moothathu, T.K.S.: Stronger forms of sensitivity for dynamical systems. Nonlinearity 20(9), 2115– 2126 (2007)
    • 16. Nia, M.F.: Parameterized IFS with the asymptotic average shadowing property. Qual. Theory Dyn. Syst. 15(2), 367–381 (2015)
    • 17. Wu, X., Chen, G.: Sensitivity and transitivity of fuzzified dynamical systems. Inf. Sci. 396, 14–23 (2017)
    • 18. Wu, X., Ding, X., Lu, T., Wang, J.: Topological dynamics of Zadeh’s extension on upper semicontinuous fuzzy sets. Int. J. Bifurc. Chaos...
    • 19. Wu, X., Wang, J., Chen, G.: F-sensitivity and multi-sensitivity of hyperspatial dynamical systems. J. Math. Anal. Appl. 429, 16–26 (2015)
    • 20. Wu, X., Wang, L., Liang, J.: The chain properties and average shadowing property of iterated function systems. Qual. Theory Dyn. Syst....
    • 21. Wu, X., Wang, X., Chen, G.: On the large deviations theorem of weaker types. Int. J. Bifurc. Chaos 27, 1750127 (2017)
    • 22. Wu, X., Zhu, P.: Devaney chaos and Li–Yorke sensitivity for product systems. Stud. Sci. Math. Hung. 49(4), 538–548 (2012)
    • 23. Wu, X., Zhu, P.: Chaos in a class of non-autonomous discrete systems. Appl. Math. Lett. 26, 431–436 (2013)

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