No abstract

No abstract

No abstract

In [6], regularly ramified rational maps are constructed and Julia sets of these maps in some one-parameter families are explored through computer-generated pictures. It is observed that they have classifications similar to the Julia sets of maps in the families f c n (z) = z n + c z n , where n ≥ 2 and c is a complex number. A new type of Julia set is also presented, which has not appeared in the literature. We call such a Julia set an exploded McMullen necklace. We prove in this paper: if a map f in the one-parameter families given in [6] has a superattracting fixed point of order greater than 2, then its Julia set J(f) is either connected, a Cantor set, or a McMullen necklace (either exploded or not); if such a map f has a superattracting fixed point of order equal to 2, then J(f) is either connected or a Cantor set.

No abstract