Ergodic Theory and Dynamical Systems

Research Article

A finiteness theorem for a dynamical class of entire functions

Lisa R. Goldberga1 and Linda Keena1

a1 C.U.N.Y., 33 West 42 Street, New York, NY 10036, USA

Abstract

We define a class Σ of entire functions whose covering properties are similar to those of rational maps. The set Σ is closed under composition of functions, and we show that when regarded as dynamical systems of the plane, the elements of Σ share many properties with rational maps. In particular, they have finite dimensional spaces of quasiconformal deformations, and they contain no wandering domains in their stable sets.

(Received April 30 1984)

(Revised January 14 1985)