{"paper":{"title":"On non-smooth slow-fast systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jaime Resende de Moraes, Paulo Ricardo da Silva","submitted_at":"2018-09-20T13:31:38Z","abstract_excerpt":"We deal with non-smooth differential systems $\\dot{z}=X(z), z\\in R^{n},$ with discontinuity occurring in a codimension one smooth surface $\\Sigma$. A regularization of $X$ is a 1-parameter family of smooth vector fields $X^{\\delta},\\delta>0$, satisfying that $X^{\\delta}$ converges pointwise to $X$ in $R^{n}\\setminus\\Sigma$, when $\\delta\\rightarrow 0$. We work with two known regularizations: the classical one proposed by Sotomayor and Teixeira and its generalization, using non-monotonic transition functions. Using the techniques of geometric singular perturbation theory we study minimal sets of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07612","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"}