On the topology of wandering Julia components
Résumé
It is known that for a rational map ƒ with a disconnected Julia set, the set of wandering Julia components is uncountable. We prove that all but countably many of them have a simple topology, namely having one or two complementary components. We show that the remaining countable subset Σ is backward invariant. Conjecturally Σ does not contain an infinite orbit. We give a very strong necessary condition for Σ to contain an infinite orbit, thus proving the conjecture for many different cases. We provide also two sufficient conditions for a Julia component to be a point. Finally we construct several examples describing different topological structures of Julia components.