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This paper discussed the control and synchronization for generalized Julia sets of the complex rational maps. First, it applied the optimal control function method on the Julia set of this system. This control method regarded infinity as a fixed point to be controlled. Then the controlled Julia set was shrinking with the controlled parameters. Second, it also studied synchronization for Julia sets with the same structure but different parameters. By substituting the response item for an item with the gradient control method, Julia set gradually changed to be another one. The simulations illustrate the efficacy of these methods by MATLAB. [ABSTRACT FROM AUTHOR]