The dynamics of nearly abelian polynomial semigroups at infinity
type: Item
instance of: scholarly article
title: The dynamics of nearly abelian polynomial semigroups at infinity
zbMATH Open document ID: 0883.30019
author: Tatsunori Harada
published in: Proceedings of the Japan Academy. Series A
publication date: 1998-03-19T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 30D05
Mathematics Subject Classification ID: 37F99
zbMATH DE Number: 1057071
zbMATH Keywords: iterated rational maps
zbMATH Keywords: dynamics
zbMATH Keywords: polynomial semigroups
reviewed by: James W. Cannon
MaRDI profile type: Publication
full work available at URL: pjaa.73.36
OpenAlex ID: W2092307529
cites work: Symmetries of Julia Sets
cites work: Poiynomials with identical Julia sets
cites work: Q4002072
cites work: The Dynamics of Semigroups of Rational Functions I
DOI: 10.3792/PJAA.73.36
description: scientific article; zbMATH DE number 1057071