Valiron, Nevanlinna and Picard exceptional sets of iterations of rational functions

Okuyama, Yûsuke

Proc. Japan Acad. Ser. A Math. Sci., Tome 81 (2005) no. 3, p. 23-26 / Harvested from Project Euclid

Résumé

For every rational function of degree more than one, there exists a transcendental meromorphic solution of the Schröder equation. By Yanagihara and Eremenko-Sodin, it is known that the Valiron, Nevanlinna and Picard exceptional sets of this solution are all same. ¶ As an analogue of this result, we show that all the Valiron, Nevanlinna and Picard exceptional sets of iterations of a rational function of degree more than one are also same. As a corollary, the equidistribution theorem in complex dynamics follows.

Publié le : 2005-02-14
Classification: Schröder equation, Valiron exceptional set, complex dynamics, equidistribution, 30D05, 39B32, 37F10

@article{1116442055,
     author = {Okuyama, Y\^usuke},
     title = {Valiron, Nevanlinna and Picard exceptional sets of iterations of rational functions},
     journal = {Proc. Japan Acad. Ser. A Math. Sci.},
     volume = {81},
     number = {3},
     year = {2005},
     pages = { 23-26},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1116442055}
}

Okuyama, Yûsuke. Valiron, Nevanlinna and Picard exceptional sets of iterations of rational functions. Proc. Japan Acad. Ser. A Math. Sci., Tome 81 (2005) no. 3, pp.  23-26. http://gdmltest.u-ga.fr/item/1116442055/