{"paper":{"title":"The dichotomy spectrum for random dynamical systems and pitchfork bifurcations with additive noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jeroen S.W. Lamb, Mark Callaway, Martin Rasmussen, Thai Son Doan","submitted_at":"2013-10-23T09:51:21Z","abstract_excerpt":"We develop the dichotomy spectrum for random dynamical system and demonstrate its use in the characterization of pitchfork bifurcations for random dynamical systems with additive noise.\n  Crauel and Flandoli had shown earlier that adding noise to a system with a deterministic pitchfork bifurcation yields a unique attracting random fixed point with negative Lyapunov exponent throughout, thus \"destroying\" this bifurcation. Indeed, we show that in this example the dynamics before and after the underlying deterministic bifurcation point are topologically equivalent.\n  However, in apparent paradox,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6166","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"}