File:SymmetricHermanRing.png
The Herman ring of some Blaschke fraction \(f(z)=e^{i2\pi\tau} z^2\frac{z-a}{1-az}\), with \(a=4\) and \(\tau\) chosen so that the restriction of \(f\) to the unit circle, which is an analytic circle diffeomorphism, has rotation number equal to the golden mean (\(\tau=0.615173215952\ldots\)). Using circle preserving rational maps, i.e. Blaschke fractions, is the easyest way to construct Herman rings.
The Julia set is in black, the Herman ring and all its iterated preimages by \(f\) are in gray. The two white components are tho basins of attraction of 0 and \(\infty\). The unit circle is in navy blue, while a few invariant curves in the Herman ring have been drawn in lighter blue.
http://i.creativecommons.org/l/by-sa/3.0/88x31.png This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. Attribution: Arnaud Chéritat.
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 21:56, 5 July 2008 | | 2,400 × 1,200 (148 KB) | Arnaud Chéritat (Talk | contribs) | The Herman ring of some Blaschke fraction <math>f(z)=e^{i2\pi\tau} z^2\frac{z-a}{1-az}</math>, with <math>a=4</math> and <math>\tau</math> chosen so that the restriction of <math>f</math> to the unit circle, which is an analytic circle diffeomorphism, has |
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