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| View Original: | Herman Standard.png (2251x1201) | |||
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| Keywords: Herman Standard.png en It's a standard image of Julia set of the rational function e<sup>2 it</sup> z<sup>2</sup> z 4 / 1 4z with t 6151732 chosen so that the rotation number is 5 1 /2 which possess a Herman ring own Yangfei math 2010-06-06 Here is an example of a rational function which possesses a Herman ring <math>f z \frac e 2 \pi i \tau z 2 z - 4 1 - 4z </math> where <math>\tau 0 6151732\dots</math> such that the rotation number of on the unit circle is <math> \sqrt 5 -1 /2</math> The picture shown on the right is the Julia set of the curves in the white annulus are the orbits of some points under the iterations of while the dashed line denotes the unit circle Herman ring of period 1 and rotation number the golden mean Compare with <gallery> File Herman-ring-1 png image of the same Julia set with src code but worse quality </gallery> References <references/> Complex analysis Mathematical theorems Herman ring Complex rational maps | ||||
