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

 

Characterizations of turbulent one-dimensional mappings via $ \omega$-limit sets


Authors: Michael J. Evans, Paul D. Humke, Cheng Ming Lee and Richard J. O’Malley
Journal: Trans. Amer. Math. Soc. 326 (1991), 261-280
MSC: Primary 58F21; Secondary 58F08, 58F13
Corrigendum: Trans. Amer. Math. Soc. 333 (1992), 939-940.
MathSciNet review: 1010884
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Abstract: The structure of $ \omega $-limit sets for nonturbulent functions is studied, and various characterizations for turbulent and chaotic functions are obtained. In particular, it is proved that a continuous function mapping a compact interval into itself is turbulent if and only if there exists an $ \omega $-limit set which is a unilaterally convergent sequence


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DOI: http://dx.doi.org/10.1090/S0002-9947-1991-1010884-3
PII: S 0002-9947(1991)1010884-3
Keywords: Turbulence, chaos, Sarkovskii stratification, $ \omega $-limit set, unilaterally convergent sequence
Article copyright: © Copyright 1991 American Mathematical Society