Scrambled sets for transitive maps. (Q595841)

The author deals with two types of chaos: the well-known chaos in the sense of Li and Yorke and the \(w\)-chaos. The author proves that every bitransitive map \(f\in C(I,I)\), where \(I= [0,1]\), is conjugate to \(g\in C(I,I)\) which satisfies the following conditions: a) there is a \(c\)-dense \(w\)-scrambled set for \(g\), b) there is an extremely in the sense of Li and Yorke scrambled set for \(g\) with full Lebesgue full measure, c) every \(w\)-scrambled set of \(g\) has zero Lebesgue measure.