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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

$ \omega$-chaos and topological entropy


Author: Shi Hai Li
Journal: Trans. Amer. Math. Soc. 339 (1993), 243-249
MSC: Primary 58F13; Secondary 58F08
MathSciNet review: 1108612
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Abstract: We present a new concept of chaos, $ \omega $-chaos, and prove some properties of $ \omega $-chaos. Then we prove that $ \omega $-chaos is equivalent to positive entropy on the interval. We also prove that $ \omega $-chaos is equivalent to the definition of chaos given by Devaney on the interval.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1108612-8
PII: S 0002-9947(1993)1108612-8
Keywords: Chaos, $ \omega $-chaos, topological entropy, minimal set, scrambled set
Article copyright: © Copyright 1993 American Mathematical Society