A Herman ring is a doubly connected periodic Fatou component on which the first-return map is holomorphically conjugate to an irrational rotation of an annulus . Compactness of the circle of rotation factors proves normality of the return iterates, and the finitely many intervening iterates preserve normality. It is the annular rotation-domain counterpart of a Siegel disc.
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A Herman ring is a concept in the field of dynamical systems, specifically in complex dynamics. It refers to a type of invariant set that arises in the study of maps, particularly those that are holomorphic or involve complex functions. A Herman ring is associated with a certain type of periodic point and is characterized by the presence of annular regions where the dynamics exhibit quasiconformal or non-unique properties.