I have met five different definitions of the Julia set and I am trying to work out why they are equivalent. I haven't managed to find a reference showing why two of these are equivalent.
Why is the boundary of the basin of attraction of $\infty$ equal to the closure of the set of repelling periodic points?
I see the connection since if $|f'(z_0)|<1$ then there is a neighbourhood of $z_0$ all of whose iterates will remain in the neighbourhood so the attracting fixed points are not even near to diverge to infinity. If $|f'(z_0)|>1$ then there is neighbourhood all of whose points except $z_0$ will "converge" to $\infty$. So the "except" case would be the boundary case?