Stability of periodic orbits in the theorem of Šarkovskii
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- by Louis Block PDF
- Proc. Amer. Math. Soc. 81 (1981), 333-336 Request permission
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
- Louis Block, Simple periodic orbits of mappings of the interval, Trans. Amer. Math. Soc. 254 (1979), 391–398. MR 539925, DOI 10.1090/S0002-9947-1979-0539925-9
- T. Y. Li and James A. Yorke, Period three implies chaos, Amer. Math. Monthly 82 (1975), no. 10, 985–992. MR 385028, DOI 10.2307/2318254 R. M. May, Simple mathematical models with very complicated dynamics, Nature 261 (1976), 459-467.
- O. M. Šarkovs′kiĭ, Co-existence of cycles of a continuous mapping of the line into itself, Ukrain. Mat. . 16 (1964), 61–71 (Russian, with English summary). MR 0159905
- P. Štefan, A theorem of Šarkovskii on the existence of periodic orbits of continuous endomorphisms of the real line, Comm. Math. Phys. 54 (1977), no. 3, 237–248. MR 445556, DOI 10.1007/BF01614086
Additional 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