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Second Descendible Self-Mapping with Closed Periodic Points Set

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DOI: 10.4236/am.2013.47133    2,238 Downloads   3,575 Views  

ABSTRACT

Let and f:XnXn be a continuous map. If f is a second descendible map, then P(f) is closed if and only if one of the following hold: 1) ; 2) For any z ε R (f), there exists a yεw (z,f) P(f) such that every point of the set orb (y,f) is a isolated point of the set w (z,f); 3) For any z ε R(f), the set w (z,f) is finite; 4) For any z ε R(f), the set w' (z,f) is finite. The consult give another condition of f with closed periodic set other than [1].

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

G. Zhang, Z. Ji and F. Zeng, "Second Descendible Self-Mapping with Closed Periodic Points Set," Applied Mathematics, Vol. 4 No. 7, 2013, pp. 969-971. doi: 10.4236/am.2013.47133.

References

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