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2001/2002 Scrambled Sets for Transitive Maps
Marek Lampart
Real Anal. Exchange 27(2): 801-808 (2001/2002).


We deal with two types of chaos: the well known chaos in the sense of Li and Yorke and $\omega$-chaos which was introduced by S. Li in 1993. In this paper we prove that every bitransitive map $f \in C(I,I)$ is conjugate to $g \in C(I,I)$, which satisfies the following conditions,

1. there is a $c$-dense $\omega$-scrambled set for $g$,

2. there is an extremely LY-scrambled set for $g$ with full Lebesgue measure,

3. every $\omega$-scrambled set of $g$ has zero Lebesgue measure.


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Marek Lampart. "Scrambled Sets for Transitive Maps." Real Anal. Exchange 27 (2) 801 - 808, 2001/2002.


Published: 2001/2002
First available in Project Euclid: 2 June 2008

zbMATH: 1062.37026
MathSciNet: MR1923170

Primary: 26A18 , 26A30 , 37D45 , 37E05 , 54H20‎

Keywords: $\omega$-chaos , LY-chaos , scrambled sets , transitive maps

Rights: Copyright © 2001 Michigan State University Press

Vol.27 • No. 2 • 2001/2002
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