{"paper":{"title":"Ground States and Zero-Temperature Measures at the Boundary of Rotation Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Christian Wolf, Tamara Kucherenko","submitted_at":"2016-04-21T23:41:04Z","abstract_excerpt":"We consider a continuous dynamical system $f:X\\to X$ on a compact metric space $X$ equipped with an $m$-dimensional continuous potential $\\Phi=(\\phi_1,\\cdots,\\phi_m):X\\to \\bR^m$. We study the set of ground states $ GS(\\alpha)$ of the potential $\\alpha\\cdot \\Phi$ as a function of the direction vector $\\alpha\\in S^{m-1}$. %We also study the corresponding rotation vectors $\\rv(GS(\\alpha))$. We show that the structure of the ground state sets is naturally related to the geometry of the generalized rotation set of $\\Phi$. In particular, for each $\\alpha$ the set of rotation vectors of $ GS(\\alpha)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06512","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"}