$napis="Abstract"; include "zacatek.inc"; ?> Preprint MA 62/2007
We study local analytic solutions f of the generalized Dhombres functional
equation f(zf(z)) = φ(f(z)), where φ is holomorphic at
w0 ≠ 0, f is holomorphic in some open neighborhood of 0, depending
on f, and f(0) = w0. After deriving necessary conditions on φ
for the existence of nonconstant solutions f with f(0) = w0 we describe,
assuming these conditions, the structure of the set of all formal solutions,
provided that w0 is not a root of 1. If |w0| ≠ 1 or if w0
is a Siegel number we show that all formal solutions yield local analytic ones.
For w0 with 0 < |w0| < 1 we give representations of these
solutions involving infinite products.
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