{"paper":{"title":"Linear response for intermittent maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.CD"],"primary_cat":"math.DS","authors_text":"M. Todd, V. Baladi","submitted_at":"2015-08-11T19:28:49Z","abstract_excerpt":"We consider the one parameter family $\\alpha \\mapsto T_\\alpha$ ($\\alpha \\in [0,1)$) of Pomeau-Manneville type interval maps $T_\\alpha(x)=x(1+2^\\alpha x^\\alpha)$ for $x \\in [0,1/2)$ and $T_\\alpha(x)=2x-1$ for $x \\in [1/2, 1]$, with the associated absolutely continuous invariant probability measure $\\mu_\\alpha$. For $\\alpha \\in (0,1)$, Sarig and Gou\\\"ezel proved that the system mixes only polynomially with rate $n^{1-1/\\alpha}$ (in particular, there is no spectral gap). We show that for any $\\psi\\in L^q$, the map $\\alpha \\to \\int_0^1 \\psi\\, d\\mu_\\alpha$ is differentiable on $[0,1-1/q)$, and we g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02700","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}