Let $f$ be a rational map with degree $d\geq 2$ 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 $\text{deg}(g)\leq 7d-2$. In particular, if $f$ is a polynomial, then $g$ can be chosen such that $\text{deg}(g)\leq 4d+4$. Moreover, some quartic and cubic rational maps whose Julia sets contain buried Jordan curves are also constructed.

中文翻译：

---

Julia 设置为埋藏的 Julia 组件

令 $f$ 为度数为 $d\geq 2$ 的有理映射，其 Julia 集连通但不等于整个黎曼球面。证明存在有理映射 $g$ 使得 $g$ 包含一个埋藏的 Julia 分量，在该分量上，当且仅当 $f$ 不具有抛物线时，该分量上的动力学与 Julia 集上的 $f$ 拟共轭盆和 Siegel 圆盘。如果这样的 $g$ 存在，那么可以选择程度使得 $\text{deg}(g)\leq 7d-2$。特别地，如果 $f$ 是多项式，则可以选择 $g$ 使得 $\text{deg}(g)\leq 4d+4$。此外，还构建了一些 Julia 集包含埋藏 Jordan 曲线的四次和三次有理映射。