ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 69, 2 (2000)
pp. 229-232

THE BITRANSITIVE CONTINUOUS MAPS OF THE INTERVAL ARE CONJUGATE TO MAPS EXTREMELY CHAOTIC A.E.
M. BABILONOVA

Abstract. 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.

AMS subject classification. 26A18, 37E05, 37D45; Secondary 54H20, 26A30, 37A25
Keywords. Bitransitive map, chaotic map, scrambled set

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Acta Mathematica Universitatis Comenianae
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Comenius University
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