JULIA SETS AS BURIED JULIA COMPONENTS

Let f be a rational map with degree d >= 2 whose Julia set is connected but not equal to the whole Riemann sphere. It is proved that there exists a rational map g such that g contains a buried Julia component on which the dynamics is quasiconformally conjugate to that of f on the Julia set if and only if f does not have parabolic basins and Siegel disks. If such g exists, then the degree can be chosen such that deg(g) <= 7d - 2. In particular, if f is a polynomial, then g can be chosen such that deg(g) <= 4d + 4. Moreover, some quartic and cubic rational maps whose Julia sets contain buried Jordan curves are also constructed.