Linear response for intermittent maps with critical point

Abstract

We consider a two-parameter family of maps Tα,β:[0,1]→[0,1] with a neutral fixed point and a non-flat critical point. Building on a cone technique due to Baladi and Todd, we show that for a class of Lq observables ϕ:[0,1]→R the bivariate map (α,β)↦∫01ϕdμα,β , where μα,β denotes the invariant SRB measure, is differentiable in a certain parameter region, and establish a formula for its directional derivative.