Ergodic Theory and Dynamical Systems

Research Article

On the measurable dynamics of zez

Etienne Ghysa1, Lisa R. Goldberga2 and Dennis P. Sullivana3

a1 Université des Sciences de Lille I 59655- Villeneuve d'Asq Cedex, France

a2 CUNY, 33 W 42nd St., New York, NY 10036, USA

a3 CUNY and IHES, 35, route de Chartres, 91 440-Bures sur Yvette, France

Abstract

We study the measure theoretic properties of the complex exponential map E(z) = ez.An particular, we show that the equivalence relation generated by E is recurrent and that E has no quasi-conformal deformations. This enables us to give some information concerning Devaney's semi-conjugacy between E and the shift map on sequences of integers.

(Received September 11 1984)

(Revised November 26 1984)