Linear response for smooth deformations of generic nonuniformly hyperbolic unimodal maps
Viviane Baladi, Daniel Smania (2012)
Annales scientifiques de l'École Normale Supérieure
Similarity:
We consider families of unimodal maps whose critical point is slowly recurrent, and we show that the unique absolutely continuous invariant measure of depends differentiably on , as a distribution of order . The proof uses transfer operators on towers whose level boundaries are mollified via smooth cutoff functions, in order to avoid artificial discontinuities. We give a new representation of for a Benedicks-Carleson map , in terms of a single smooth function and the...