A note on non-converging Julia sets

We consider a sequence of entire functions converging to a limit function g locally uniformly on . It is claimed by Kisaka that, if the Fatou set F(g) of the limit function is the union of the basins of attracting periodic orbits, then the Julia sets converge to the Julia set J(g) in the Hausdorff metric. We show that this is not true in general.