A chaotic function possessing a scrambled set with positive Lebesgue measure
Author:
I. Kan
Journal:
Proc. Amer. Math. Soc. 92 (1984), 45-49
MSC:
Primary 26A30; Secondary 58F13
DOI:
https://doi.org/10.1090/S0002-9939-1984-0749887-4
MathSciNet review:
749887
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Abstract | References | Similar Articles | Additional Information
Abstract: A continuous function, chaotic in the sense of Li and Yorke, is constructed which possesses a scrambled set of positive Lebesgue measure.
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- J. Smítal, A chaotic function with some extremal properties, Proc. Amer. Math. Soc. 87 (1983), no. 1, 54–56. MR 677230, DOI https://doi.org/10.1090/S0002-9939-1983-0677230-7
- Motosige Osikawa and Yoshitsugu Oono, Chaos in $C^{0}$-endomorphism of interval, Publ. Res. Inst. Math. Sci. 17 (1981), no. 1, 165–177. MR 613940, DOI https://doi.org/10.2977/prims/1195186710
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- Jean-Pierre Kahane and Raphaël Salem, Ensembles parfaits et séries trigonométriques, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1301, Hermann, Paris, 1963 (French). MR 0160065
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Additional Information
Keywords:
Chaos,
scrambled sets
Article copyright:
© Copyright 1984
American Mathematical Society