{"paper":{"title":"Linear response theory for diffeomorphisms with tangencies of stable and unstable manifolds. [A contribution to the Gallavotti-Cohen chaotic hypothesis.]","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"David Ruelle","submitted_at":"2018-05-15T17:07:45Z","abstract_excerpt":"This note presents a non-rigorous study of the linear response for an SRB (or `natural physical') measure $\\rho$ of a diffeomorphism $f$ in the presence of tangencies of the stable and unstable manifolds of $\\rho$. We propose that generically, if $\\rho$ has no zero Lyapunov exponent, if its stable dimension is sufficiently large (greater than 1/2 or perhaps 3/2) and if it is exponentially mixing in a suitable sense, then the following formal expression for the first derivative of $\\rho(\\phi)$ with respect to $f$ along $X$ is convergent: $$ \\Psi(z)=\\sum_{n=0}^\\infty z^n\\int\\rho(dx)\\,X(x)\\cdot\\n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.05910","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"}