Ergodic Theory and Dynamical Systems

Table of Contents - 01 March 1992 - Volume 12, Issue 01  

Research Article

Absolutely continuous invariant measures and random perturbations for certain one-dimensional maps

Michael Benedicksa1 and Lai-Sang Younga2†

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

Abstract

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)

Footnotes

† 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.