Hartje Kriete, Hiroki Sumi
Semihyperbolic transcentental semigroups
Preprint series: Mathematica Gottingensis
30D05 Functional equations in the complex domain, iteration and composition of analytic functions, See also {34A20, 39-XX, 58F08, 58F23}
54H20 Topological dynamics, See also {28Dxx, 34C35, 58Fxx}
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