## Kodai Mathematical Journal

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

### Linearization problem on structurally finite entire functions

#### 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**

https://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. https://projecteuclid.org/euclid.kmj/1123767015