Simple proofs of some fundamental properties of the Julia set

Let f be a holomorphic self-map of C\{0}, C or the extended complex plane ( C) over bar that is neither injective nor constant. This paper gives new an d elementary proofs of the well-known fact that the Julia set of f is a non -empty perfect set and coincides with the closure of the set of repelling c ycles of f. The proofs use Montel-Caratheodory's theorem but do not use res ults from Nevanlinna theory.