Ergodic Theory and Dynamical Systems

Research Article

Topology and growth of a special class of holomorphic self-maps of *

Linda Keena1

a1 Department of Mathematics, Lehman College, Bronx, New York, 10468, USA


It is a general problem to find appropriate sets of moduli for families of functions that generate dynamical systems. In this paper we solve this problem for a specific family of holomorphic self-maps of * defined by


The main theorem states that any function topologically conjugate to a member of is holomorphically conjugate to some member of the family. It follows that the coefficients of the polynomials P(z) and Q(z) are a suitable set of moduli for the families of dynamical systems generated by these functions.

The moduli spaces of functions in are easy to study computationally and have been studied by many authors. (See references in the text.)

(Received October 05 1987)

(Revised June 02 1988)


† Research supported in part by NSF grant #DMS-8503015.