{"paper":{"title":"Periods of orbits for maps on graphs homotopic to a constant map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Adriana Johnson, Chris Bernhardt, Whitney Radil, Zach Gaslowitz","submitted_at":"2011-08-14T18:59:13Z","abstract_excerpt":"The paper proves two theorems concerning the set of periods of periodic orbits for maps of graphs that are homotopic to the constant map and such that the vertices form a periodic orbit. The first result is that if $v$ is not a divisor of $2^k$ then there must be a periodic point with period $2^k$. The second is that if $v=2^ks$ for odd $s>1$, then for all $r>s$ there exists a periodic point of minimum period $2^k r$. These results are then compared to the Sharkovsky ordering of the positive integers.\n  (The final version of this paper will appear in the Journal of Difference Equations and App"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2899","kind":"arxiv","version":3},"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"}