Michael Benedicks:Parameter selection in one-dimensional maps revisited

Abstract. There are several ways to co construct abundance (positive
measure) of parameters with absolutely continuous invariant measures for
one-dimensional maps. The first is the famous construction due to
Jakobson. Another is due to Carleson and myself in the case of the
quadratic family. I will discuss this later proof in the view of its basic
ingredients and which generalizations may be possible  i.e. to circle maps 
and iterations of complex quadratic polynomials (last topic is joint work with Jacek Graczyk.)