{"paper":{"title":"On the smooth dependence of SRB measures for partially hyperbolic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Zhiyuan Zhang","submitted_at":"2017-01-18T22:47:48Z","abstract_excerpt":"In this paper, we study the differentiability of SRB measures for partially hyperbolic systems. We show that for any $s \\geq 1$, for any integer $\\ell \\geq 2$, any sufficiently large $r$, any $\\varphi \\in C^{r}(\\T, \\R)$ such that the map $f : \\T^2 \\to \\T^2, f(x,y) = (\\ell x, y + \\varphi(x))$ is $C^r-$stably ergodic, there exists an open neighbourhood of $f$ in $C^r(\\T^2,\\T^2)$ such that any map in this neighbourhood has a unique SRB measure with $C^{s-1}$ density, which depends on the dynamics in a $C^s$ fashion. We also construct a $C^{\\infty}$ mostly contracting partially hyperbolic diffeomo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05253","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"}