{"paper":{"title":"Selection of calibrated subaction when temperature goes to zero in the discounted problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.DS","authors_text":"Artur O. Lopes, Jairo K. Mengue, Renato Iturriaga","submitted_at":"2017-10-16T19:59:53Z","abstract_excerpt":"Consider $T(x)= d \\, x$ (mod 1) acting on $S^1$, a Lipschitz potential $A:S^1 \\to \\mathbb{R}$, $0<\\lambda<1$ and the unique function $b_\\lambda:S^1 \\to \\mathbb{R}$ satisfying $ b_\\lambda(x) = \\max_{T(y)=x} \\{ \\lambda \\, b_\\lambda(y) + A(y)\\}.$\n  We will show that, when $\\lambda \\to 1$, the function $b_\\lambda- \\frac{m(A)}{1-\\lambda}$ converges uniformly to the calibrated subaction $V(x) = \\max_{\\mu \\in \\mathcal{ M}} \\int S(y,x) \\, d \\mu(y)$, where $S$ is the Ma\\~ne potential, $\\mathcal{ M}$ is the set of invariant probabilities with support on the Aubry set and $m(A)= \\sup_{\\mu \\in \\mathcal{M}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05974","kind":"arxiv","version":2},"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"}