{"paper":{"title":"On dendrites, generated by polyhedral systems and their ramification points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.MG","authors_text":"Andrei Tetenov, Dmitry Vaulin, Mary Samuel","submitted_at":"2017-07-07T16:34:25Z","abstract_excerpt":"The paper considers systems of contraction similarities in $\\mathbb R^d$ sending a given polyhedron $P$ to polyhedra $P_i\\subset P$, whose non-empty intersections are singletons and contain the common vertices of those polyhedra, while the intersection hypergraph of the system is acyclic. It is proved that the attractor $K$ of such system is a dendrite in $\\mathbb R^d$. The ramification points of such dendrite fave finite order whose upper bound depends only on the polyhedron $P$, and the set of the cut points of the dendrite $K$ is equal to the dimension of the whole $K$ iff $K$ is a Jordan a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02875","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":""},"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"}