On the left is a plot of L2(x) for the unstable 2-cycle
above.
The magnification on the right shows that both fixed points of L2(x)
constituting the 2-cycle of L(x) are unstable: the graph
of L2(x) crosses the fixed points outside the bowties, though the
seeing this for the left side of the upper fixed point wold be easier under higher
magnification.