The local connectivity of the Julia sets of rational maps is one of the central themes in complex dynamics. In this talk we show that a long iteration of rational maps is expansive near boundaries of bounded type Siegel disks. This leads us to extend Petersen's local connectivity result on the Julia sets of quadratic Siegel polynomials to a general case. A new key feature in the proof is that the puzzles are not used. This is a joint work with Shuyi Wang, Gaofei Zhang and Yanhua Zhang.