{"paper":{"title":"Aperiodic points in $\\mathbb Z^2$-subshifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"cs.DM","authors_text":"Anael Grandjean, Benjamin Hellouin de Menibus, Pascal Vanier","submitted_at":"2018-05-22T19:37:14Z","abstract_excerpt":"We consider the structure of aperiodic points in $\\mathbb Z^2$-subshifts, and in particular the positions at which they fail to be periodic. We prove that if a $\\mathbb Z^2$-subshift contains points whose smallest period is arbitrarily large, then it contains an aperiodic point. This lets us characterise the computational difficulty of deciding if an $\\mathbb Z^2$-subshift of finite type contains an aperiodic point. Another consequence is that $\\mathbb Z^2$-subshifts with no aperiodic point have a very strong dynamical structure and are almost topologically conjugate to some $\\mathbb Z$-subshi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.08829","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"}