{"paper":{"title":"Linear and fractional response for the SRB measure of smooth hyperbolic attractors and discontinuous observables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.CD"],"primary_cat":"math.DS","authors_text":"Tobias Kuna, Valerio Lucarini, Viviane Baladi","submitted_at":"2016-03-31T17:20:02Z","abstract_excerpt":"We consider a smooth one-parameter family $t \\to f_t$ of diffeomorphisms with compact transitive Axiom A attractors. Our first result (corrected) is that for any function $G$ in the Sobolev space $H^r_p$, with $p>1$ and $0<r<1/p$, the map $R(t)$ sending $t$ to the average of $G$ with respect to the SRB measure of $f_t$ is $\\alpha$-H\\\"older continuous for all $\\alpha <r- |log \\mathcal J|/(p|log \\nu_s|$) where $\\mathcal J\\le 1$ is the strongest volume contraction and $\\nu_s<1$ is the weakest contraction. This applies to $\\theta(x)=h(x)\\Theta(g(x)-a)$ (for all $\\alpha <1- |log \\mathcal J|/|log \\n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.09690","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"}