## Characterizations of weakly chaotic maps of the interval

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- by V. V. Fedorenko, A. N. Šarkovskii and J. Smítal
- Proc. Amer. Math. Soc.
**110**(1990), 141-148 - DOI: https://doi.org/10.1090/S0002-9939-1990-1017846-5
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## Abstract:

We prove, among others, the following relations between notions of chaos for continuous maps of the interval: (i) A map $f$ is not chaotic in the sense of Li and Yorke iff $f$ restricted to the set of its $\omega$-limit points is stable in the sense of Ljapunov. (ii) The topological entropy of $f$ is zero iff $f$ restricted to the set of chain recurrent points is not chaotic in the sense of Li and Yorke, and this is iff every trajectory is approximable by trajectories of periodic intervals.## References

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## Bibliographic Information

- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**110**(1990), 141-148 - MSC: Primary 58F20; Secondary 28D20, 54H20, 58F08, 58F13
- DOI: https://doi.org/10.1090/S0002-9939-1990-1017846-5
- MathSciNet review: 1017846