{"paper":{"title":"Dimension approximation of attractors of graph directed IFSs by self-similar sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"\\'Abel Farkas","submitted_at":"2015-05-21T14:10:27Z","abstract_excerpt":"We show that for the attractor $(K_{1},\\dots,K_{q})$ of a graph directed iterated function system, for each $1\\leq j\\leq q$ and $\\varepsilon>0$ there exits a self-similar set $K\\subseteq K_{j}$ that satisfies the strong separation condition and $\\dim_{H}K_{j}-\\varepsilon<\\dim_{H}K$. We show that we can further assume convenient conditions on the orthogonal parts and similarity ratios of the defining similarities of $K$. Using this property as a `black box' we obtain results on a range of topics including on dimensions of projections, intersections, distance sets and sums and products of sets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05746","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"}