Linearization problem on structurally finite entire functions
Complex Variables
2012-01-09 v2 Dynamical Systems
Abstract
We show that if a 1-hyperbolic structurally finite entire function of type , , 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 -subhyperbolicity naturally arises.
Cite
@article{arxiv.math/0408222,
title = {Linearization problem on structurally finite entire functions},
author = {Yûsuke Okuyama},
journal= {arXiv preprint arXiv:math/0408222},
year = {2012}
}
Comments
14pages, AMSLaTeX, to appear in Kodai Mathematical Journal