We show that the second rational map $G$ associated with the group $\mathcal{G}$ of intermediate growth constructed by the first author in 1980 is semiconjugate with the antiholomorphic map $z\rightarrow\bar{z}^2$. For doing this we use a family of $G$--invariant curves found by the third author and for each invariant curve, create a Markov partition of it.

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