Paper detail

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

We consider a family of Pomeau-Manneville type interval maps $T_α$, parametrized by $α\in (0,1)$, with the unique absolutely continuous invariant probability measures $ν_α$, and rate of correlations decay $n^{1-1/α}$. We show that despite the absence of a spectral gap for all $α\in (0,1)$ and despite nonsummable correlations for $α\geq 1/2$, the map $α\mapsto \int φ\, dν_α$ is continuously differentiable for $φ\in L^{q}[0,1]$ for $q$ sufficiently large.