The Yoccoz U function
These pictures relate to the Yoccoz U function.
J.-C. Yoccoz, Astérisque 231 (1995), page 70; and
An introduction to small divisors problems (2000),
page 19 for more details.
The function u(l) is defined by
u0=1/2; un+1=un-ln/2 un2 (n=0,1,2,...)
The series begins
u(l) = 1/2-l/8-l2/8+....
I computed 1000 terms of the power series of U
by exact rational arithmetic, summed the series with high-precision
real arithmetic, and created the graphics with R.
Radial limit of U
arg(U) inside unit circle
abs(U) inside unit circle
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