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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0593484-8
PII: S 0002-9939(1981)0593484-8
Keywords: Periodic point, period of a periodic point
Article copyright: © Copyright 1981 American Mathematical Society