{"paper":{"title":"Multiple reductions, foliations and the dynamics of cluster maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Helena Mena-Matos, In\\^es Cruz, M. Esmeralda Sousa-Dias","submitted_at":"2016-07-13T10:00:59Z","abstract_excerpt":"Presymplectic and Poisson reduction of cluster maps are described in terms of the \"canonical\" foliations of presymplectic and Poisson manifolds. This approach to reduction leads to a geometric description, in terms of foliations, of the dynamics of the original (not reduced) map. The case where multiple reductions exist (presymplectic/Poisson or presymplectic/Poisson/Poisson) is further explored and examples illustrating several features of this approach are presented, including a nontrivial one in dimension seven which is comprehensively treated."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03664","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"}