{"paper":{"title":"Automorphisms of the shift: Lyapunov exponents, entropy, and the dimension representation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Scott Schmieding","submitted_at":"2018-03-11T22:48:20Z","abstract_excerpt":"Let $(X_{A},\\sigma_{A})$ be a shift of finite type and $\\text{Aut}(\\sigma_{A})$ its corresponding automorphism group. Associated to $\\phi \\in \\text{Aut}(\\sigma_{A})$ are certain Lyapunov exponents $\\alpha^{-}(\\phi), \\alpha^{+}(\\phi)$ which describe asymptotic behavior of the sequence of coding ranges of $\\phi^{n}$. We give lower bounds on $\\alpha^{-}(\\phi), \\alpha^{+}(\\phi)$ in terms of the spectral radius of the corresponding action of $\\phi$ on the dimension group associated to $(X_{A},\\sigma_{A})$. We also give lower bounds on the topological entropy $h_{top}(\\phi)$ in terms of a distinguis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04060","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"}