Abstract
We show that if a 1-hyperbolic structurally finite entire function of type (p, q), p ≥ 1, is linearizable at an irrationally indifferent fixed point, then its multiplier satisfies the Brjuno condition. We also prove the generalized Mañé 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.
Citation
Yûsuke Okuyama. "Linearization problem on structurally finite entire functions." Kodai Math. J. 28 (2) 347 - 358, June 2005. https://doi.org/10.2996/kmj/1123767015
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