Kodai Mathematical Journal

Linearization problem on structurally finite entire functions

Yûsuke Okuyama

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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.

Article information

Source
Kodai Math. J. Volume 28, Number 2 (2005), 347-358.

Dates
First available in Project Euclid: 11 August 2005

Permanent link to this document
http://projecteuclid.org/euclid.kmj/1123767015

Digital Object Identifier
doi:10.2996/kmj/1123767015

Mathematical Reviews number (MathSciNet)
MR2153922

Citation

Okuyama, Yûsuke. Linearization problem on structurally finite entire functions. Kodai Math. J. 28 (2005), no. 2, 347--358. doi:10.2996/kmj/1123767015. http://projecteuclid.org/euclid.kmj/1123767015.


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