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

Published online by Cambridge University Press:  19 September 2008

Michael Benedicks  and
Lai-Sang Young
Michael Benedicks
Affiliation:
Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden
Lai-Sang Young
Affiliation:
Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA, and Department of Mathematics, UCLA, Los Angeles, CA 90024, USA
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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 12 , Issue 1 , March 1992 , pp. 13 - 37
Copyright
Copyright © Cambridge University Press 1992

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References

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