Linearization problem on structurally finite entire functions
Okuyama, Yûsuke
Kodai Math. J., Tome 28 (2005) no. 1, p. 347-358 / Harvested from Project Euclid
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.
Publié le : 2005-06-14
Classification: 
@article{1123767015,
     author = {Okuyama, Y\^usuke},
     title = {Linearization problem on structurally finite entire functions},
     journal = {Kodai Math. J.},
     volume = {28},
     number = {1},
     year = {2005},
     pages = { 347-358},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1123767015}
}
Okuyama, Yûsuke. Linearization problem on structurally finite entire functions. Kodai Math. J., Tome 28 (2005) no. 1, pp.  347-358. http://gdmltest.u-ga.fr/item/1123767015/