{"paper":{"title":"Orbit equivalent substitution dynamical systems and complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"O. Karpel, S. Bezuglyi","submitted_at":"2012-01-08T10:50:43Z","abstract_excerpt":"For any primitive proper substitution \\sigma, we give explicit constructions of countably many pairwise non-isomorphic substitution dynamical systems {(X_{\\zeta_n}, T_{\\zeta_n})}_{n=1}^{\\infty} such that they all are (strong) orbit equivalent to (X_{\\sigma}, T_{\\sigma}). We show that the complexity of the substitution dynamical systems {(X_{\\zeta_n}, T_{\\zeta_n})} is essentially different that prevents them from being isomorphic. Given a primitive (not necessarily proper) substitution \\tau, we find a stationary simple properly ordered Bratteli diagram with the least possible number of vertices"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1622","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"}