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
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)