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Stability of periodic orbits in the theorem of Šarkovskii


Author: Louis Block
Journal: Proc. Amer. Math. Soc. 81 (1981), 333-336
MSC: Primary 58F20; Secondary 28D05
DOI: https://doi.org/10.1090/S0002-9939-1981-0593484-8
MathSciNet review: 593484
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Abstract: Let $ f$ be a continuous map of a closed, bounded interval into itself. It is shown that the conclusion of the theorem of Sarkovskii holds for perturbations of $ f$. In other words, if $ f$ has a periodic point of period $ k$, and $ g$ is a continuous map close to $ f$, then $ g$ has periodic points of certain periods.


References [Enhancements On Off] (What's this?)

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  • [4] A. N. Šarkovskii, Coexistence of cycles of a continuous map of a line into itself, Ukrain. Mat. Ž. 16 (1964), 61-71. MR 0159905 (28:3121)
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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0593484-8
Keywords: Periodic point, period of a periodic point
Article copyright: © Copyright 1981 American Mathematical Society

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