a1 Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden
a2 Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA, and Department of Mathematics, UCLA, Los Angeles, CA 90024, USA
We study the quadratic family and show that for a positive measure set of parameters the map has an absolutely continuous invariant measure that is stable under small random perturbations.
(Received June 21 1990)
(Revised February 14 1991)
† The authors gratefully acknowledge the hospitality of IAS at Princeton, where most of this work was done. Benedicks is partially supported by the Swedish Natural Science Research Council (NFR) and the Swedish Board of Technical Development (STU). Young is partially supported by NSF.