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Sharkovskii's order and the stability of periodic points of maps of the interval

Published online by Cambridge University Press:  09 April 2009

Guang Yuan Zhang  and
Qing Zhong Li
Guang Yuan Zhang
Affiliation:
Department of Mathematical Sciences Tsinghua University Beijing 100084 P. R. China e-mail: gyzhang@mail.tsinghua.edu.cn
Qing Zhong Li
Affiliation:
Department of Mathematics Capital Normal University Beijing 100037 P. R. China e-mail: qzhli@mail.cnu.edu.cn
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Abstract

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Let f be a Cr (r ≥ 0) map from the interval [0, 1] into itself and m be a positive integer. This paper gives a sufficient and necessary condition under which the set of periodic points of period m disappears after a certain small Cr-perturbation.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 68 , Issue 2 , April 2000 , pp. 244 - 251
Copyright
Copyright © Australian Mathematical Society 2000

References

[B]Block, L., ‘Stability of the periodic orbits in the theorem of Sharkovskii’, Proc. Amer. Math. Soc. 81 (1981), 333–336.Google Scholar
[D]Dugundji, J., Topology (Allyn and Bacon, Boston, 1966).Google Scholar
[S]Sharkovskii, A. N., ‘Coexistence of cycles of a continuous map of the line into itself’, Ukrain. Mat. Zh. 16 (1964), 61–71.Google Scholar