Linear response for intermittent maps with summable and nonsummable decay of correlations

Abstract

We consider a family of Pomeau-Manneville type interval maps Tα, parametrized by α ∈ (0, 1), with the unique absolutely continuous invariant probability measures να, and rate of correlations decay n 1−1/α. We show that despite the absence of a spectral gap for all α ∈ (0, 1) and despite nonsummable correlations for α ≥ 1/2, the map α 7→ R ϕ dνα is continuously differentiable for ϕ ∈ L q [0, 1] for q sufficiently large.