{"paper":{"title":"On Conjugacy Invariants of $D_{\\infty}$-Topological Markov Chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Sieye Ryu","submitted_at":"2014-07-15T13:30:17Z","abstract_excerpt":"A $D_{\\infty}$-topological Markov chain can be represented by a pair of zero-one square matrices, which is called a flip pair. We introduce the concepts of $D_{\\infty}$-strong shift equivalence and $D_{\\infty}$-shift equivalence, which are equivalence relations between flip pairs. We investigate the relationships between the existence of a $D_{\\infty}$-conjugacy, the existence of a $D_{\\infty}$-strong shift equivalence, the existence of a $D_{\\infty}$-shift equivalence and the coincidence of the Lind zeta functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3988","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"}