A regularity result for fixed points, with applications to linear response. (5th March 2018) - Sedro, Julien
Abstract: In this paper, we show a series of abstract results on fixed point regularity with respect to a parameter. They are based on a Taylor development taking into account a loss of regularity phenomenon, typically occurring for composition operators acting on spaces of functions with finite regularity. We generalize this approach to higher order differentiability, through the notion of an n-graded family . We then give applications to the fixed point of a nonlinear map, and to linear response in the context of (uniformly) expanding dynamics (theorem7 and corollary20 ), in the spirit of Gouëzel–Liverani.