Hartje Kriete, Hiroki Sumi
Semihyperbolic transcentental semigroups
Preprint series: Mathematica Gottingensis

MSC:

30D05 Functional equations in the complex domain, iteration and composition of analytic functions

54H20 Topological dynamics

Abstract: This paer deals with semihyperbolic semigroups which are generated by
entire (possibly transcentental) 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.

Keywords: complex dynamic, iteration, Julia set, Fatou set, semigroup, semihyperbolic, transcendental function