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Dynamics in One Complex Variable. (AM-160), 3rd Edition by John Milnor

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§15. Herman Rings

This section will be a survey, without complete proofs, describing a close relative of the Siegel disk.

Definition. A component U of the Fatou set image \ J(f) is called a Herman ring if U is conformally isomorphic to some annulus

image

and if f, or some iterate of f, corresponds to an irrational rotation of this annulus. (Siegel disks and Herman rings are often collectively called rotation domains.)

There are two known methods for constructing Herman rings. The original method, due to Herman [1979], is based on a careful analysis of real ...

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