{"paper":{"title":"On the convergence to equilibrium of unbounded observables under a family of intermittent interval maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Johannes Kautzsch, Marc Kesseb\\\"ohmer, Tony Samuel","submitted_at":"2014-10-14T19:17:27Z","abstract_excerpt":"We consider a family $\\{ T_{r} \\colon [0, 1] \\circlearrowleft \\}_{r \\in [0, 1]}$ of Markov interval maps interpolating between the Tent map $T_{0}$ and the Farey map $T_{1}$. Letting $\\mathcal{P}_{r}$ denote the Perron-Frobenius operator of $T_{r}$, we show, for $\\beta \\in [0, 1]$ and $\\alpha \\in (0, 1)$, that the asymptotic behaviour of the iterates of $\\mathcal{P}_{r}$ applied to observables with a singularity at $\\beta$ of order $\\alpha$ is dependent on the structure of the $\\omega$-limit set of $\\beta$ with respect to $T_{r}$. Having a singularity it seems that such observables do not fall"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3805","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"}