On holomorphic families of rational maps: Finiteness, rigidity and stability (Q5940257)

We consider holomorphic families of rational maps from the viewpoint of complex dynamics. First, we consider some classes of families of rational maps that satisfy a certain stability condition. We show a finiteness theorem for such holomorphic families of rational maps parametrized by a Riemann surface of finite type. Next we consider the monodromy of quasiconformally stable holomorphic families of rational maps over the punctured disk, and study the action of the monodromy on the Julia set.