Some "Theorem" on the generalized superfunction

[JmsNxn]

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Leo, I agree precisely with what you just said. I was glazing over complex details; and speaking a little loose. I suggest reading Milnor though; your half iterate exists and can be constructed. There always exists a half iterate about any fixed poin \( |f'(L)| = 1 \) where \( f'(L) = e^{2\pi i \frac{p}{q}} \).

The trouble is; we need to choose the half iterate appropriately; and it maps petals to petals. And there exists multiplie n roots; and multiples of this based on q. Please look at Ecalle; I can't say it any better.