Geodesic
THE BITRANSITIVE CONTINUOUS MAPS OF THE INTERVAL ARE CONJUGATE TO MAPS EXTREMELY CHAOTIC A.E.
Acta mathematica Universitatis Comenianae, Tome 69 (2000) no. 2 
M. Babilonova. THE BITRANSITIVE CONTINUOUS MAPS OF THE INTERVAL ARE CONJUGATE TO MAPS EXTREMELY CHAOTIC A.E.. Acta mathematica Universitatis Comenianae, Tome 69 (2000) no. 2. http://geodesic.mathdoc.fr/item/AMUC_2000_69_2_a7/
@article{AMUC_2000_69_2_a7,
     author = {M. Babilonova},
     title = {THE {BITRANSITIVE} {CONTINUOUS} {MAPS} {OF} {THE} {INTERVAL} {ARE} {CONJUGATE} {TO} {MAPS} {EXTREMELY} {CHAOTIC} {A.E.}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2000},
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Voir la notice de l'article provenant de la source Comenius University

In the eighties, Misiurewicz, Bruckner and Hu provided examples of functions chaotic almost everywhere. In this paper we show - by using much simpler arguments - that any bitransitive continuous map of the interval is conjugate to a map which is extremely chaotic almost everywhere. Using a result of A. M. Blokh we get as a consequence that for any map $f$ with positive topological entropy there is a $k$ such that $f^k$ is semiconjugate to a continuous map which is extremely chaotic almost everywhere.