September  2003, 9(5): 1323-1327. doi: 10.3934/dcds.2003.9.1323

Omega-chaos almost everywhere

1. 

Mathematical Institute, Silesian University, 746 01 Opava, Czech Republic, Czech Republic

Received  August 2002 Revised  January 2003 Published  June 2003

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.
Citation: Jaroslav Smítal, Marta Štefánková. Omega-chaos almost everywhere. Discrete & Continuous Dynamical Systems - A, 2003, 9 (5) : 1323-1327. doi: 10.3934/dcds.2003.9.1323
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