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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Positive sequence topological entropy characterizes chaotic maps


Authors: N. Franzová and J. Smítal
Journal: Proc. Amer. Math. Soc. 112 (1991), 1083-1086
MSC: Primary 58F13; Secondary 28D20, 54H20, 58F11
MathSciNet review: 1062387
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Abstract: We prove that a continuous map $ f$ of the interval is chaotic (in the sense of Li and Yorke) iff its sequence topological entropy $ {h_A}(f)$ relative to a suitable increasing sequence $ A$ of times is positive. This result is interesting since the ordinary topological entropy $ h(f)$ of chaotic maps can be zero.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1062387-3
PII: S 0002-9939(1991)1062387-3
Article copyright: © Copyright 1991 American Mathematical Society