{"paper":{"title":"The dynamical system generated by the floor function $\\lfloor\\lambda x\\rfloor$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"I.A. Sattarov, J.B. Usmonov, U.A. Rozikov","submitted_at":"2015-03-24T18:22:48Z","abstract_excerpt":"We investigate the dynamical system generated by the function $\\lfloor\\lambda x\\rfloor$ defined on $\\mathbb R$ and with a parameter $\\lambda\\in \\mathbb R$. For each given $m\\in \\mathbb N$ we show that there exists a region of values of $\\lambda$, where the function has exactly $m$ fixed points (which are non-negative integers), also there is another region for $\\lambda$, where there are exactly $m+1$ fixed points (which are non-positive integers). Moreover the full set $\\mathbb Z$ of integer numbers is the set of fixed points iff $\\lambda=1$. We show that depending on $\\lambda$ and on the init"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07129","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"}