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Journal of the London Mathematical Society 2004 69(1):201-213; doi:10.1112/S0024610703004691
© 2004 by London Mathematical Society
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© The London Mathematical Society

The Immediate Basin of Attraction of Infinity for Polynomial Semigroups of Finite Type

David A. Boyd

Department of Mathematics, Washington State University Pullman, WA 99164, USA, boyd{at}math.wsu.edu

Received 25 July 2002. Revision received 29 April 2003.

As a generalization of the dynamics of a single polynomial, Hinkkanen and Martin studied the dynamics of polynomial semigroups of finite type. Among the issues addressed were possible generalizations of the filled-in Julia set of a single polynomial and the basin of attraction for infinity. In the paper, these concepts are further refined, and the connections between the dynamics of a single function and the dynamics of semigroups are strengthened.


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