{"paper":{"title":"A cell decomposition for marked cycle curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Caroline Davis, Danny Stoll, Giulio Tiozzo, Malavika Mukundan","submitted_at":"2024-10-28T14:03:49Z","abstract_excerpt":"We describe a family $\\textrm{Cyc}_p(\\mathcal{F})$ of marked cycle curves that parameterize the cycles of period $p$ of a given family $\\mathcal{F}$ of dynamical systems. We produce algorithms to compute a canonical cell decomposition for the marked cycle curves over the family $\\textrm{Per}_1(0)$ of quadratic polynomials as well as over the family $\\textrm{Per}_2(0)$ of quadratic rational maps with a critical 2-cycle. We obtain formulas for the number of $d$-cells in these decompositions, giving rise to e.g. a formula for their genus."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.21049","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.21049/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}