{"paper":{"title":"The natural measure of a symbolic dynamical system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Song-Sun Lin, Wen-Guei Hu","submitted_at":"2013-08-13T23:59:55Z","abstract_excerpt":"This study investigates the natural or intrinsic measure of a symbolic dynamical system $\\Sigma$. The measure $\\mu([i_{1},i_{2},...,i_{n}])$ of a pattern $[i_{1},i_{2},...,i_{n}]$ in $\\Sigma$ is an asymptotic ratio of $[i_{1},i_{2},...,i_{n}]$, which arises in all patterns of length $n$ within very long patterns, such that in a typical long pattern, the pattern $[i_{1},i_{2},...,i_{n}]$ appears with frequency $\\mu([i_{1},i_{2},...,i_{n}])$. When $\\Sigma=\\Sigma(A)$ is a shift of finite type and $A$ is an irreducible $N\\times N$ non-negative matrix, the measure $\\mu$ is the Parry measure. $\\mu$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2996","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"}