Ergodic Theory and Dynamical Systems

Research Article

Some entire functions with multiply-connected wandering domains

I. N. Bakera1

a1 Department of Mathematics, Imperial College of Science and Technology, University of London, London SW7 2BZ, England

Abstract

A component U of the complement of the Julia set of an entire function ƒ is a wandering domain if the sets ƒn(U) are mutually disjoint, where n ℕ and ƒn is the n-th iterate of ƒ. Examples are given of entire ƒ of order , which have multiply-connected wandering domains. An example is given where the connectivity is infinite.

(Received September 27 1984)

(Revised November 26 1984)