  In this paper, we give a family of rational maps whose Julia sets are Cantor
circles and show that every rational map whose Julia set is a Cantor set of
circles must be topologically conjugate to one map in this family on their
corresponding Julia sets. In particular, we give the specific expressions of
some rational maps whose Julia sets are Cantor circles, but they are not
topologically conjugate to any McMullen maps on their Julia sets. Moreover,
some non-hyperbolic rational maps whose Julia sets are Cantor circles are also
constructed.
