{"paper":{"title":"Heteroclinic Cycles in Systems with $\\mathbb{Z}_2\\times\\mathbb{Z}_2\\times\\mathbb{Z}_2$ Symmetry, Revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Adrian C. Murza","submitted_at":"2016-11-08T00:28:26Z","abstract_excerpt":"We analyze the generating mechanisms for heteroclinic cycles in $\\mathbb{Z}_2\\times\\mathbb{Z}_2\\times\\mathbb{Z}_2$--equivariant ODEs, not involving Hopf bifurcations. Such cycles have been observed in particle physics systems with the mentioned symmetry, in absence of the Hopf bifurcation, see \\cite{bury} and \\cite{Park}, and as far as we know, there is no available theoretical data explaining these phenomena. We use singularity theory to study the equivalence in the group-symmetric context, as well as the recognition problem for the simplest bifurcation problems with this symmetry group. Sing"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02349","kind":"arxiv","version":4},"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"}