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.
Citation
Hartje Kriete. Hiroki Sumi. "Semihyperbolic transcendental semigroups." J. Math. Kyoto Univ. 40 (2) 205 - 216, 2000. https://doi.org/10.1215/kjm/1250517712
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