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Omega-chaos almost everywhere

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  • Developping ideas of S. Li [Tran. Amer. Math. Soc. 301 (1993), 243--249] concerning the notion of $\omega$-chaos we prove that any transitive continuous map $f$ of the interval is conjugate to a map $g$ of the interval which possesses an $\omega$-scrambled set $S$ of full Lebesgue measure. Thus, for any distinct $x, y$ in $S$, $\omega _g (x)\cap\omega _g(y)$ is non-empty, and $\omega _g(x) \setminus\omega _g(y)$ is uncountable.
    Mathematics Subject Classification: Primary: 26A18, 37D45, 37E05; Secondary: 54H20, 26A30, 37A25.


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