{"paper":{"title":"Singularities of the susceptibility of an SRB measure in the presence of stable-unstable tangencies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"David Ruelle","submitted_at":"2010-01-30T14:13:05Z","abstract_excerpt":"Let $\\rho$ be an SRB (or \"physical\"), measure for the discrete time evolution given by a map $f$, and let $\\rho(A)$ denote the expectation value of a smooth function $A$. If $f$ depends on a parameter, the derivative $\\delta\\rho(A)$ of $\\rho(A)$ with respect to the parameter is formally given by the value of the so-called susceptibility function $\\Psi(z)$ at $z=1$. When $f$ is a uniformly hyperbolic diffeomorphism, it has been proved that the power series $\\Psi(z)$ has a radius of convergence $r(\\Psi)>1$, and that $\\delta\\rho(A)=\\Psi(1)$, but it is known that $r(\\Psi)<1$ in some other cases. O"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0067","kind":"arxiv","version":1},"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"}