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# The construction of chaotic maps in the sense of Devaney on dendrites which commute to continuous maps on the unit interval

• Let $f$ be a continuous map from the unit interval to itself. In this paper, it is shown that $f$ has positive topological entropy if and only if $f$ is pointwise $P$-expansive for some periodic orbit $P$ of $f$. And it is also proved that if $f$ has a periodic orbit with odd period, then there exists a chaotic map from a dendrite to itself in the sense of Devaney which is semiconjugate to $f$ and has positive topological entropy.
Mathematics Subject Classification: 54H20, 37B40, 37E05, 54F50.

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