{"paper":{"title":"Canard Cycles and Poincar\\'e Index of Non-Smooth Vector Fields on the Plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Claudio Buzzi, Paulo Ricardo da Silva, Tiago De Carvalho","submitted_at":"2010-02-22T19:13:17Z","abstract_excerpt":"This paper is concerned with closed orbits of non-smooth vector fields on the plane. For a subclass of non-smooth vector fields we provide necessary and sufficient conditions for the existence of canard kind solutions. By means of a regularization we prove that the canard cycles are singular orbits of singular perturbation problems which are limit periodic sets of a sequence of limit cycles. Moreover, we generalize the Poincar\\'e Index for non-smooth vector fields."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.4169","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"}