{ "id": "2410.11465", "version": "v1", "published": "2024-10-15T10:13:24.000Z", "updated": "2024-10-15T10:13:24.000Z", "title": "Singular points in generic two-parameter families of vector fields on 2-manifold", "authors": [ "Dmitry A. Filimonov", "Yulij S. Ilyashenko" ], "categories": [ "math.DS" ], "abstract": "In this paper, we give a full description of all possible singular points that occur in generic 2-parameter families of vector fields on compact 2-manifolds. This is a part of a large project aimed to a complete study of global bifurcations in two-parameter families of vector fields on the two-sphere.", "revisions": [ { "version": "v1", "updated": "2024-10-15T10:13:24.000Z" } ], "analyses": { "subjects": [ "37G10", "58K45", "34C23" ], "keywords": [ "vector fields", "generic two-parameter families", "singular points", "global bifurcations", "complete study" ], "note": { "typesetting": "TeX", "pages": 0, "language": "en", "license": "arXiv", "status": "editable" } } }