Linearization problem on structurally finite entire functions

Details Linearization problem on structurally finite entire functions Linearization problem on structurally finite entire functions

2004-08-17

arxiv.org/abs/math/0408222v2

Kodai Math. J., 28, No. 2 (2005), 347-358

Mathematics

Complex Variables

14pages, AMSLaTeX, to appear in Kodai Mathematical Journal

Scientific paper

10.2996/kmj/1123767015

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.

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