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05-02
Yusuke OKUYAMA

*Linearization problem on structurally finite entire functions*

### Abstract

We show that if a 1-hyperbolic structurally finite entire function
of type $(p,q)$, $p\ge 1$, is linearizable at an irrationally
indifferent fixed point, then its multiplier satisfies the Brjuno
condition. We also prove the generalized Ma\~n\'e theorem;
if an entire function has only finitely many critical points and
asymptotic values, then for every such a non-expanding forward invariant set
that is either a Cremer cycle or the boundary of a cycle of Siegel disks,
there exists an asymptotic value or a recurrent critical point such that
the derived set of its forward orbit contains this invariant set.
From it, the concept of $n$-subhyperbolicity naturally arises.

submission: 15 May, 2005

to appear in Kodai Math J.

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