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We extend a theorem of Herman from the case of unicritical polynomials to thecase of polynomials with two finite critical values. This theorem states thatSiegel disks of such polynomials, under a diophantine condition (calledHerman's condition) on the rotation number, must have a critical point on theirboundaries.

Herman's condition and critical points on the boundary of Siegel disks of polynomials with two critical values