Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Entire functions with Julia sets of zero measure

Gwyneth M. Stallarda1

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


We extend results of McMullen about the dynamics of entire functions for which the orbits of the critical values stay away from the Julia set. In particular we show that such functions are expanding on their Julia sets which have self-similarity properties. Under suitable further conditions the Julia sets have plane measure zero.

(Received July 21 1989)

(Revised February 21 1990)