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

Abstract

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

arXiv commentCorrected and improved technical estimates; minor general corrections