{"paper":{"title":"Projections of cartesian products of the self-similar sets without the irrationality assumption","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Kan Jiang","submitted_at":"2018-06-04T12:48:55Z","abstract_excerpt":"Let $\\beta>1$. Define a class of similitudes \\[S=\\left\\{f_{i}(x)=\\dfrac{x}{\\beta^{n_i}}+a_i:n_i\\in \\mathbb{N}^{+}, a_i\\in \\mathbb{R}\\right\\}.\\] Let $\\mathcal{A}$ be the collection of all the self-similar sets generated by the similitudes from $S$. In this paper, we prove that for any $\\theta\\in(0,\\pi)$ and $K_1, K_2\\in \\mathcal{A}$, $Proj_{\\theta}(K_1\\times K_2)$ is similar to a self-similar set or an attractor of some infinite iterated function system, where $Proj_{\\theta}$ denotes the orthogonal projection onto $L_{\\theta}$, and $L_{\\theta}$ denotes the line through the origin in direction $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.01080","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"}