Stability of periodic orbits in the theorem of Šarkovskii
- 1 February 1981
- journal article
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 81 (2) , 333-336
- https://doi.org/10.1090/s0002-9939-1981-0593484-8
Abstract
Let f 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 f . In other words, if f f has a periodic point of period k k , and g g is a continuous map close to f f , then g g has periodic points of certain periods.Keywords
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