Source: Proc. Japan Acad. Ser. A Math. Sci. Volume 81, Number 2
(2005), 23-26.
For every rational function of degree more than one, there
exists a transcendental meromorphic solution of the Schröder
equation. By Yanagihara and Eremenko-Sodin, it is known that
the Valiron, Nevanlinna and Picard exceptional sets of this
solution are all same.
As an analogue of this result,
we show that all the Valiron, Nevanlinna and Picard exceptional
sets of iterations of a rational function of degree more than
one are also same. As a corollary, the equidistribution theorem
in complex dynamics follows.
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