The dynamics of nearly abelian polynomial semigroups at infinity (Q1364453)

The author proves that a nearly abelian polynomial semigroup which contains some polynomials of degree at least two is analytically conjugate near infinity to a subsemigroup of \(\langle z\to az^n\rangle\), where \(a\) is a complex constant of modulus 1 and \(n\) runs through the positive integers. When \textit{A. Hinkkanen} and \textit{G. J. Martin} [Proc. Lond. Math. Soc., III. Ser. 73, 358-384 (1996; Zbl 0859.30026)] began the development of the dynamics of semigroups of rational functions, they picked out the nearly abelian polynomial semigroups as some to which the classical dynamical results generalize. The current result, which verifies one of their conjectures, helps to justify their intuitions.