Connectivity of Filled Julia Sets for Quartic Polynomials

By the extend Puzzle technique of Branner-Hubbard and Yoccoz to study the filled Julia sets of a kind of quartic polynomials f,obtaining that a connected component of the filled Julia sets is non-trivial(that is,it has two points at least) if and only if it is a periodic critical component,or an inverse image of some periodic critical component under the iteration of f.