## Journal of Mathematics of Kyoto University

### Semihyperbolic transcendental semigroups

#### Abstract

This paper deals with semihyperbolic semigroups which are generated by entire (possibly transcendental) functions. In particular, a criterion is given assuring that a given entire semigroup is semihyperbolic. Note that a semihyperbolic semigroup $G$ admits holomorphic scaling, that is to say, the branches of local inverses of functions $f \in G$ are of bounded degree and that the preimages shrink to zero in diameter.

#### Article information

Source
J. Math. Kyoto Univ., Volume 40, Number 2 (2000), 205-216.

Dates
First available in Project Euclid: 17 August 2009

https://projecteuclid.org/euclid.kjm/1250517712

Digital Object Identifier
doi:10.1215/kjm/1250517712

Mathematical Reviews number (MathSciNet)
MR1787870

Zentralblatt MATH identifier
0992.37036

#### Citation

Kriete, Hartje; Sumi, Hiroki. Semihyperbolic transcendental semigroups. J. Math. Kyoto Univ. 40 (2000), no. 2, 205--216. doi:10.1215/kjm/1250517712. https://projecteuclid.org/euclid.kjm/1250517712