Given a rational map $f:\overline{ \mathbb C}\to \overline{ \mathbb C}$ and a finite graph $G\subset \overline{ \mathbb C}$ such that $f(G)\subset G$ and $f$ is expanding on some neighbourhood of $G$, we show that there is another finite graph $G'\subset \bigcup _{ n\ge 0}f^{ -n}(G)$ in an arbitrarily small neighbourhood of $G$ such that $f^N(G')\subset G'$ for some integer $N$ but $\bigcup _{ i=0}^{ N-1}f^{ i}(G')$ contains accumulating { \em{ plaits}} and { \em{ nests}}
Categories: math.DS