{"paper":{"title":"Connectedness of attractors of a certain family of IFSs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Filip Strobin, Jaros{\\l}aw Swaczyna","submitted_at":"2018-12-16T09:19:51Z","abstract_excerpt":"Let $X$ be a Banach space and $f,g:X\\rightarrow X$ be contractions. We investigate the set $$ C_{f,g}:=\\{w\\in X:\\m{ the attractor of IFS }\\F_w=\\{f,g+w\\}\\m{ is connected}\\}. $$ The motivation for our research comes from papers of Mihail and Miculescu, where it was shown that $C_{f,g}$ is a countable union of compact sets, provided $f,g$ are linear bounded operators with $\\pa f\\pa,\\pa g\\pa<1$ and such that $f$ is compact. Moreover, in the case when $X$ is finitely dimensional, such sets have been intensively investigated in the last years, especially when $f$ and $g$ are affine maps. As we will "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.06427","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"}