{"paper":{"title":"A dichotomy theorem for minimizers of monotone recurrence relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Blaz Mramor, Bob Rink","submitted_at":"2011-11-25T12:43:56Z","abstract_excerpt":"Variational monotone recurrence relations arise in solid state physics as generalizations of the Frenkel-Kontorova model for a ferromagnetic crystal. For such problems, Aubry-Mather theory establishes the existence of \"ground states\" or \"global minimizers\" of arbitrary rotation number.\n  A nearest neighbor crystal model is equivalent to a Hamiltonian twist map. In this case, the global minimizers have a special property: they can only cross once. As a nontrivial consequence, every one of them has the Birkhoff property. In crystals with a larger range of interaction and for higher order recurre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5970","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"}