{"paper":{"title":"Dimension of homogeneous iterated function systems with algebraic translations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"De-Jun Feng, Zhou Feng","submitted_at":"2024-05-06T02:42:01Z","abstract_excerpt":"Let $ \\mu $ be the self-similar measure associated with a homogeneous iterated function system $ \\Phi = \\{ \\lambda x + t_j \\}_{j=1}^m $ on ${\\Bbb R}$ and a probability vector $ (p_{j})_{j=1}^m$, where $0\\neq \\lambda\\in (-1,1)$ and $t_j\\in {\\Bbb R}$. Recently by modifying the arguments of Varj\\'u (2019), Rapaport and Varj\\'u (2024) showed that if $t_1,\\ldots, t_m$ are rational numbers and $0<\\lambda<1$, then $$ \\dim \\mu =\\min\\Big \\{ 1, \\; \\frac{\\sum_{j=1}^m p_{j}\\log p_{j}}{ \\log |\\lambda| }\\Big\\}$$ unless $ \\Phi $ has exact overlaps. In this paper, we further show that the above equality holds"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.03124","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/2405.03124/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"}