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Linear response for smooth deformations of generic nonuniformly hyperbolic unimodal maps

Viviane BaladiDaniel Smania — 2012

Annales scientifiques de l'École Normale Supérieure

We consider C 2 families t f t of  C 4 unimodal maps f t whose critical point is slowly recurrent, and we show that the unique absolutely continuous invariant measure μ t of  f t depends differentiably on  t , as a distribution of order 1 . 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  μ t for a Benedicks-Carleson map f t , in terms of a single smooth function and the inverse branches...

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