Characterizations of weakly chaotic maps of the interval

Authors:
V. V. Fedorenko, A. N. Šarkovskii and J. Smítal

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

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove, among others, the following relations between notions of chaos for continuous maps of the interval: (i) A map is not chaotic in the sense of Li and Yorke iff restricted to the set of its -limit points is stable in the sense of Ljapunov. (ii) The topological entropy of is zero iff 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.

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DOI:
https://doi.org/10.1090/S0002-9939-1990-1017846-5

Article copyright:
© Copyright 1990
American Mathematical Society