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Common periodic trajectories of two mappings

For a mapping fC r(I, I), r ≥ 0, we consider the problem of the existence of a mapping close to it that has periodic trajectories of given periods in common with f.

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References

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    M. Polezzi and C. Aniz, “A Sharkovskii-type theorem for pairs of mappings,” Far East J. Dynam. Syst., 7, No. 1, 65–75 (2005).

  2. 2.

    A. N. Sharkovskii, S. F. Kolyada, A. G. Sivak, and V. V. Fedorenko, Dynamics of One-Dimensional Mappings [in Russian], Naukova Dumka, Kiev (1989).

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    A. N. Sharkovskii, “On cycles and structure of a continuous mapping,” Ukr. Mat. Zh., 17, No. 3, 40–41 (1965).

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Author information

Correspondence to M. Yu. Matviichuk.

Additional information

Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 7, pp. 937–948, July, 2008.

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Matviichuk, M.Y. Common periodic trajectories of two mappings. Ukr Math J 60, 1099–1113 (2008). https://doi.org/10.1007/s11253-008-0119-3

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Keywords

  • Natural Number
  • Stationary Point
  • Periodic Point
  • Common Point
  • Periodic Trajectory