{"paper":{"title":"Radon--Nikodym representations of Cuntz--Krieger algebras and Lyapunov spectra for KMS states","license":"","headline":"","cross_cats":["math.OA"],"primary_cat":"math.DS","authors_text":"Bernd O. Stratmann, Manuel Stadlbauer, Marc Kesseb\\\"ohmer","submitted_at":"2006-01-15T17:14:58Z","abstract_excerpt":"We study relations between $(H,\\beta)$--KMS states on Cuntz--Krieger algebras and the dual of the Perron--Frobenius operator $\\mathcal{L}_{-\\beta H}^{*}$. Generalising the well--studied purely hyperbolic situation, we obtain under mild conditions that for an expansive dynamical system there is a one--one correspondence between $(H,\\beta)$--KMS states and eigenmeasures of $\\mathcal{L}_{-\\beta H}^{*}$ for the eigenvalue 1. We then consider representations of Cuntz--Krieger algebras which are induced by Markov fibred systems, and show that if the associated incidence matrix is irreducible then th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0601354","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"}