{"paper":{"title":"Attractivity, degeneracy and codimension of a typical singularity in 3D piecewise smooth vector fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Marco Antonio Teixeira, Tiago De Carvalho","submitted_at":"2015-08-03T15:44:42Z","abstract_excerpt":"We address the problem of understanding the dynamics around typical singular points of $3D$ piecewise smooth vector fields. A model $Z_0$ in $3D$ presenting a T-singularity is considered and a complete picture of its dynamics is obtained in the following way: \\textit{(i)} $Z_0$ has an invariant plane $\\pi_0$ filled up with periodic orbits (this means that the restriction $Z_0 |_{\\pi_0}$ is a center around the singularity), \\textit{(ii)} All trajectories of $Z_0$ converge to the surface $\\pi_0$, and such attraction occurs in a very non-usual and amazing way, \\textit{(iii)} given an arbitrary in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00456","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"}