{"paper":{"title":"Slow--fast systems and sliding on codimension 2 switching manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Paulo Ricardo da Silva, Willian Pereira Nunes","submitted_at":"2018-08-23T23:46:45Z","abstract_excerpt":"In this work we consider piecewise smooth vector fields $X$ defined in $\\R^n\\setminus \\Sigma$, where $\\Sigma$ is a self-intersecting switching manifold. A double regularization of $X$ is a 2-parameter family of smooth vector fields $X_{\\e.\\eta}$, $\\e,\\eta>0,$ satisfying that $X_{\\e,\\eta}$ converges pointwise to $X$ on $\\R^n\\setminus\\Sigma$, when $\\e,\\eta\\rightarrow 0$. We define the sliding region on the non regular part of $\\Sigma$ as a limit of invariant manifolds of $X_{\\e.\\eta}$. Since the double regularization provides a slow--fast system, the GSP-theory (geometric singular perturbation t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.07968","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"}