Herman ring

In the mathematical discipline known as complex dynamics, the Herman ring is a Fatou component where the rational function is conformally conjugate to an irrational rotation of the standard annulus.

Namely if ƒ possesses a Herman ring U with period p, then there exists a conformal mapping

and an irrational number ${\displaystyle \theta }$, such that

So the dynamics on the Herman ring is simple.

It was introduced by, and later named after, Michael Herman (1979) who first found and constructed this type of Fatou component.

Here is an example of a rational function which possesses a Herman ring.

where ${\displaystyle \tau =0.6151732\dots }$ such that the rotation number of ƒ on the unit circle is ${\displaystyle ({\sqrt {5}}-1)/2}$.

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