{"paper":{"title":"Density of periodic points, invariant measures and almost equicontinuous points of cellular automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Pierre Tisseur (CMCC)","submitted_at":"2006-08-10T06:50:14Z","abstract_excerpt":"Revisiting the notion of m-almost equicontinuous cellular automata introduced by R. Gilman, we show that the sequence of image measures of a shift ergodic measure m by iterations of a m-almost equicontinuous automata F, converges in Cesaro mean to an invariant measure mc. If the initial measure m is a Bernouilli measure, we prove that the Cesaro mean limit measure mc is shift mixing. Therefore we also show that for any shift ergodic and F-invariant measure m, the existence of m-almost equicontinuous points implies that the set of periodic points is dense in the topological support S(m) of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0608240","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"}