  It is known that the disconnected Julia set of any polynomial map does not
contain buried Julia components. But such Julia components may arise for
rational maps. The first example is due to Curtis T. McMullen who provided a
family of rational maps for which the Julia sets are Cantor of Jordan curves.
However all known examples of buried Julia components, up to now, are points or
Jordan curves and comes from rational maps of degree at least 5.
  This paper introduce a family of hyperbolic rational maps with disconnected
Julia set whose exchanging dynamics of postcritically separating Julia
components is encoded by a weighted dynamical tree. Each of these Julia sets
presents buried Julia components of several types: points, Jordan curves, but
also Julia components which are neither points nor Jordan curves. Moreover this
family contains some rational maps of degree 3 with explicit formula that
answers a question McMullen raised.

Dynamical Systems