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For the family of quadratic rational functions having a $2$-cycle of boundedtype Siegel disks, we prove that each of the boundaries of these Siegel diskscontains at most one critical point. In the parameter plane, we prove that thelocus for which the boundaries of the $2$-cycle of Siegel disks contain twocritical points is a Jordan curve.

Quadratic rational maps with a $2$-cycle of Siegel disks