On Sets Where Iterates of a Meromorphic Function Zip Towards Infinity

For a transcendental meromorphic function f, various propertiesof the set formula] were obtained in 8] and 9]. Here we establish analogous propertiesfor the smaller sets formula] introduced in 5], and formula] We deduce a symmetry result for Julia sets J(f), and also indicatesome techniques for showing that certain invariant curves liein I'(f), Z(f) and J(f). 2000 Mathematics Subject Classification30D05, 37F10, 37F50.