{"paper":{"title":"Ulam's method for computing stationary densities of invariant measures for piecewise convex maps with countably infinite number of branches","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"A H M Mahbubur Rahman, Md Shafiqul Islam, Pawe{\\l} G\\'ora","submitted_at":"2024-05-04T18:16:20Z","abstract_excerpt":"Let $\\tau: I=[0, 1]\\to [0, 1]$ be a piecewise convex map with countably infinite number of branches. In \\cite{GIR}, the existence of absolutely continuous invariant measure (ACIM) $\\mu$ for $\\tau$ and the exactness of the system $(\\tau, \\mu)$ has been proven. In this paper, we develop an Ulam method for approximation of $f^*$, the density of ACIM $\\mu$. We construct a sequence $\\{\\tau_n\\}_{n=1}^\\infty$ of maps $\\tau_n: I\\to I$ s. t. $\\tau_n$ has a finite number of branches and the sequence $\\tau_n$ converges to $\\tau$ almost uniformly. Using supremum norms and Lasota-Yorke type inequalities, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.02729","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.02729/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"}