{"paper":{"title":"(G,\\mu)- Quadratic Stochastic Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"J. Blath, M.Scheutzow, U.U. Jamilov","submitted_at":"2013-07-04T10:38:47Z","abstract_excerpt":"We consider a new subclass of quadratic stochastic (evolutionary) operators on the simplex indexed by a finite Abelian group G with heredity law \\mu. With the help of the notion of s(\\mu)-invariant subgroups, where s(\\mu) denotes the support of \\mu in G, we prove that almost all (w.r.t.\\ Lebesgue measure) trajectories of such operators converge to a unique fixed point which is the center of the simplex. We also identify and describe the periodic trajectories of the operator and give conditions for regularity and periodicity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1265","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"}