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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Stability of periodic orbits in the theorem of Šarkovskii
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by Louis Block
Proc. Amer. Math. Soc. 81 (1981), 333-336
DOI: https://doi.org/10.1090/S0002-9939-1981-0593484-8

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
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Bibliographic Information
  • © Copyright 1981 American Mathematical Society
  • 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