## Journal of Mathematics of Kyoto University

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

### 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

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.1215/kjm/1250517712

**Mathematical Reviews number (MathSciNet)**

MR1787870

**Zentralblatt MATH identifier**

0992.37036

**Subjects**

Primary: 37F10: Polynomials; rational maps; entire and meromorphic functions [See also 32A10, 32A20, 32H02, 32H04]

Secondary: 30D05: Functional equations in the complex domain, iteration and composition of analytic functions [See also 34Mxx, 37Fxx, 39-XX] 37F15: Expanding maps; hyperbolicity; structural stability 37F50: Small divisors, rotation domains and linearization; Fatou and Julia sets

#### 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