English

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 (p,q)(p,q), p1p\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 nn-subhyperbolicity naturally arises.

Keywords

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