{"paper":{"title":"Spectral and dynamical results related to certain non-integer base expansions on the unit interval","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP"],"primary_cat":"math.SP","authors_text":"Giovanna Marcelli, Horia D. Cornean, Ira W. Herbst","submitted_at":"2025-02-10T14:26:44Z","abstract_excerpt":"We consider certain non-integer base $\\beta$-expansions of Parry's type and we study various properties of the transfer (Perron-Frobenius) operator $\\mathcal{P}:L^p([0,1])\\mapsto L^p([0,1])$ with $p\\geq 1$ and its associated composition (Koopman) operator, which are induced by a discrete dynamical system on the unit interval related to these $\\beta$-expansions. We show that if $f$ is Lipschitz, then the iterated sequence $\\{\\mathcal{P}^N f\\}_{N\\geq 1}$ converges exponentially fast (in the $L^1$ norm) to an invariant state corresponding to the eigenvalue $1$ of $\\mathcal{P}$. This \"attracting\" "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.06511","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.06511/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}