{"paper":{"title":"Asymptotic stability at infinity for bidimensional Hurwitz vector fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Roland Rabanal","submitted_at":"2007-04-11T13:49:23Z","abstract_excerpt":"Let $X:U-->R^2$ be a differentiable vector field. Set $Spc(X)={eigenvalues of DX(z) : z\\in U}$. This $X$ is called Hurwitz if $Spc(X)\\subset{z\\in C:\\Re(z)<0}$. Suppose that $X$ is Hurwitz and $U\\subset R^2$ is the complement of a compact set. Then by adding to $X$ a constant $v$ one obtains that the infinity is either an attractor or a repellor for $X+v.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.1418","kind":"arxiv","version":4},"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"}