06/09/2011, 05:56 AM
(06/08/2011, 10:58 PM)mike3 Wrote: Anyway, I think this is not analytic at 0. The iterates of g so formed have a branch point at 0, and also a complementary one at infinity (note that if there is a BP at 0, there must be one at inf, since "circling about inf" is equivalent to circling about 0). The conjugate simply exchanges these two branch points. This would explain how it can approachas
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Well, the behaviour is comparable to that of
Even [1] shows that that there is no solution of f(f(x))=ax^2+bx+c in the complex plane.
[1] Rice, R. E., Schweizer, B., & Sklar, A. (1980). When is $f(f(z))=az^2+bz+c$? Am. Math. Mon., 87, 252–263.